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Physics Semester I Final Review ConcepTest 3.2a Vector Components I 1) it doubles If each component of a 2) it increases, but by less than double vector is doubled, what 3) it does not change happens to the angle of 4) it is reduced by half that vector? 5) it decreases, but not as much as half ConcepTest 3.2a Vector Components I 1) it doubles If each component of a 2) it increases, but by less than double vector is doubled, what 3) it does not change happens to the angle of 4) it is reduced by half that vector? 5) it decreases, but not as much as half The magnitude of the vector clearly doubles if each of its components is doubled. But the angle of the vector is given by tan q = 2y/2x, which is the same as tan q = y/x (the original angle). Follow-up: If you double one component and not the other, how would the angle change? ConcepTest 3.4a Firing Balls I A small cart is 1) it depends on how fast the cart is moving rolling at constant 2) it falls behind the cart velocity on a flat track. it falls in front of the cart 3) It fires a ball straight 4) it falls right back into the cart up into the air as it 5) it remains at rest moves. After it is fired, what happens to the ball? ConcepTest 3.4a Firing Balls I A small cart is rolling at 1) it depends on how fast the cart is constant velocity on a flat moving track. It fires a ball straight 2) it falls behind the cart up into the air as it moves. 3) it falls in front of the cart After it is fired, what happens 4) it falls right back into the cart to the ball? 5) it remains at rest In the frame of reference of the cart, the ball only has a vertical component of velocity. So it goes up and comes back down. To a ground observer, both the when when cart and the ball have the viewed from viewed from same horizontal velocity, velocity train ground so the ball still returns into the cart. ConcepTest 3.4b Firing Balls II Now the cart is being pulled 1) it depends upon how much the along a horizontal track by an track is tilted external force (a weight hanging over the table edge) 2) it falls behind the cart and accelerating. It fires a ball 3) it falls in front of the cart straight out of the cannon as it moves. After it is fired, what 4) it falls right back into the cart happens to the ball? 5) it remains at rest ConcepTest 3.4b Firing Balls II Now the cart is being pulled 1) it depends upon how much the along a horizontal track by an track is tilted external force (a weight hanging over the table edge) 2) it falls behind the cart and accelerating. It fires a ball 3) it falls in front of the cart straight out of the cannon as it moves. After it is fired, what 4) it falls right back into the cart happens to the ball? 5) it remains at rest Now the acceleration of the cart is completely unrelated to the ball. In fact, the ball does not have any horizontal acceleration at all (just like the first question), so it will lag behind the accelerating cart once it is shot out of the cannon. ConcepTest 3.4c Firing Balls III The same small cart is now rolling down an 1) it depends upon how much the track is tilted inclined track and 2) it falls behind the cart accelerating. It fires a ball straight out of the 3) it falls in front of the cart cannon as it moves. 4) it falls right back into the cart After it is fired, what happens to the ball? 5) it remains at rest ConcepTest 3.4c Firing Balls III The same small cart is now rolling down an 1) it depends upon how much the track is tilted inclined track and 2) it falls behind the cart accelerating. It fires a ball straight out of the 3) it falls in front of the cart cannon as it moves. 4) it falls right back into the cart After it is fired, what happens to the ball? 5) it remains at rest Because the track is inclined, the cart accelerates. However, the ball has the same component of acceleration along the track as the cart does! This is essentially the component of g acting parallel to the inclined track. So the ball is effectively accelerating down the incline, just as the cart is, and it falls back into the cart. ConcepTest 3.5 Dropping a Package You drop a package from 1) quickly lag behind the plane while falling a plane flying at constant 2) remain vertically under the speed in a straight line. plane while falling 3) move ahead of the plane while Without air resistance, falling the package will: 4) not fall at all ConcepTest 3.5 Dropping a Package You drop a package from 1) quickly lag behind the plane while falling a plane flying at constant 2) remain vertically under the speed in a straight line. plane while falling 3) move ahead of the plane while Without air resistance, falling the package will: 4) not fall at all Both the plane and the package have the same horizontal velocity at the moment of release. They will maintain this velocity in the x- direction, so they stay aligned. direction Follow-up: What would happen if air resistance were present? ConcepTest 3.6a Dropping the Ball I 1) the “dropped” ball From the same height 2) the “fired” ball (and at the same time), 3) they both hit at the same time one ball is dropped and 4) it depends on how hard the ball was fired another ball is fired 5) it depends on the initial height horizontally. Which one will hit the ground first? ConcepTest 3.6a Dropping the Ball I From the same height 1) the “dropped” ball (and at the same time), 2) the “fired” ball one ball is dropped and 3) they both hit at the same time another ball is fired 4) it depends on how hard the ball horizontally. Which one was fired will hit the ground first? 5) it depends on the initial height Both of the balls are falling vertically under the influence of gravity. They both fall from the same height. Therefore, they will hit the ground at the same time. The fact that one is moving horizontally is irrelevant – remember that the x and y motions are completely independent !! Follow-up: Is that also true if there is air resistance? ConcepTest 3.6b Dropping the Ball II In the previous problem,1) the “dropped” ball 2) the “fired” ball which ball has the 3) neither – they both have the same velocity on impact greater velocity at 4) it depends on how hard the ground level? ball was thrown ConcepTest 3.6b Dropping the Ball II In the previous problem, 1) the “dropped” ball 2) the “fired” ball which ball has the 3) neither – they both have the greater velocity at same velocity on impact ground level? 4) it depends on how hard the ball was thrown Both balls have the same vertical velocity when they hit the ground (since they are both acted on by gravity for the same time). However, the “fired” ball also has a horizontal velocity. When you add the two components vectorially, the “fired” ball has a larger net velocity when it hits the ground. Follow-up: What would you have to do to have them both reach the same final velocity at ground level? ConcepTest 3.6c Dropping the Ball III 1) just after it is launched A projectile is 2) at the highest point in its flight launched from the 3) just before it hits the ground ground at an angle of 30o. At what point in 4) halfway between the ground and the highest point its trajectory does 5) speed is always constant this projectile have the least speed? ConcepTest 3.6c Dropping the Ball III 1) just after it is launched A projectile is launched from the ground at an 2) at the highest point in its flight angle of 30o. At what 3) just before it hits the ground point in its trajectory 4) halfway between the ground and does this projectile the highest point have the least speed? 5) speed is always constant The speed is smallest at the highest point of its flight path because the y- component of the velocity is zero. zero ConcepTest 4.1a Newton’s First Law I 1) there is a net force but the book has too A book is lying at much inertia rest on a table. 2) there are no forces acting on it at all The book will 3) it does move, but too slowly to be seen 4) there is no net force on the book remain there at 5) there is a net force, but the book is too rest because: heavy to move ConcepTest 4.1a Newton’s First Law I 1) there is a net force but the book has too A book is lying at much inertia rest on a table. 2) there are no forces acting on it at all The book will 3) it does move, but too slowly to be seen 4) there is no net force on the book remain there at 5) there is a net force, but the book is too rest because: heavy to move There are forces acting on the book, but the only book forces acting are in the y-direction. Gravity acts downward, but the table exerts an upward force that is equally strong, so the two forces cancel, leaving no net force. force ConcepTest 4.1b Newton’s First Law II A hockey 1) more than its weight puck slides 2) equal to its weight on ice at 3) less than its weight but more than zero 4) depends on the speed of the puck constant 5) zero velocity. What is the net force acting on the puck? ConcepTest 4.1b Newton’s First Law II A hockey puck 1) more than its weight slides on ice at 2) equal to its weight constant velocity. 3) less than its weight but more than zero What is the net 4) depends on the speed of the puck force acting on the 5) zero puck? The puck is moving at a constant velocity, and velocity therefore it is not accelerating. Thus, there must accelerating be no net force acting on the puck. Follow-up: Are there any forces acting on the puck? What are they? ConcepTest 4.7a Gravity and Weight I 1) Fg is greater on the feather What can you 2) Fg is greater on the stone say about the 3) Fg is zero on both due to vacuum 4) Fg is equal on both always force of 5) Fg is zero on both always gravity Fg acting on a stone and a feather? ConcepTest 4.7a Gravity and Weight I 1) Fg is greater on the feather What can you say 2) Fg is greater on the stone about the force of 3) Fg is zero on both due to vacuum 4) Fg is equal on both always gravity Fg acting 5) Fg is zero on both always on a stone and a feather? The force of gravity (weight) depends on the mass of the object!! The stone has more mass, therefore more weight. ConcepTest 4.7b Gravity and Weight II 1) it is greater on the feather What can you 2) it is greater on the stone say about the 3) it is zero on both due to vacuum 4) it is equal on both always acceleration of 5) it is zero on both always gravity acting on the stone and the feather? ConcepTest 4.7b Gravity and Weight II What can you say 1) it is greater on the feather about the acceleration 2) it is greater on the stone 3) it is zero on both due to vacuum of gravity acting on 4) it is equal on both always the stone and the 5) it is zero on both always feather? The acceleration is given by F/m so here the mass divides out. Since we know that the force of gravity (weight) is mg, then we end up with acceleration mg g for both objects. Follow-up: Which one hits the bottom first? ConcepTest 4.9a Going Up I A block of mass m rests on the floor of 1) N > mg an elevator that is moving upward at 2) N = mg constant speed. What is the 3) N < mg (but not zero) relationship between the force due to gravity and the normal force on the 4) N = 0 block? 5) depends on the size of the elevator v m ConcepTest 4.9a Going Up I A block of mass m rests on the floor of 1) N > mg an elevator that is moving upward at 2) N = mg constant speed. What is the 3) N < mg (but not zero) relationship between the force due to gravity and the normal force on the 4) N = 0 block? 5) depends on the size of the elevator The block is moving at constant speed, so it must have no net force on it. The forces v on it are N (up) and mg (down), so N = mg, mg just like the block at rest on a table. m ConcepTest 4.9b Going Up II A block of mass m rests 1) N > mg 2) N = mg on the floor of an 3) N < mg (but not zero) elevator that is 4) N = 0 accelerating upward. 5) depends on the size of the What is the relationship elevator between the force due to gravity and the normal a force on the block? m ConcepTest 4.9b Going Up II A block of mass m rests on the 1) N > mg floor of an elevator that is 2) N = mg accelerating upward. What is 3) N < mg (but not zero) the relationship between the 4) N = 0 force due to gravity and the 5) depends on the size of the normal force on the block? elevator The block is accelerating upward, so N it must have a net upward force. The force m forces on it are N (up) and mg (down), a>0 mg so N must be greater than mg in order to give the net upward force! force S F = N – mg = ma > 0 Follow-up: What is the normal force if \ N > mg the elevator is in free fall downward? ConcepTest 4.10 Normal Force 1) case 1 Below you see two 2) case 2 cases: a physics 3) it’s the same for both student pulling or 4) depends on the magnitude of pushing a sled with a the force F force F which is 5) depends on the ice surface applied at an angle q. Case 1 In which case is the normal force greater? Case 2 ConcepTest 4.10 Normal Force Below you see two cases: 1) case 1 a physics student pulling or 2) case 2 pushing a sled with a force 3) it’s the same for both F which is applied at an 4) depends on the magnitude of angle q. In which case is the the force F normal force greater? 5) depends on the ice surface Case 1 In Case 1, the force F is pushing down (in addition to mg), so the normal force mg needs to be larger. In Case 2, the force F larger Case 2 is pulling up, against gravity, so the up normal force is lessened. lessened ConcepTest 4.11 On an Incline Consider two identical blocks, 1) case A one resting on a flat surface 2) case B and the other resting on an 3) both the same (N = mg) incline. For which case is the normal force greater? 4) both the same (0 < N < mg) 5) both the same (N = 0) A B ConcepTest 4.11 On an Incline Consider two identical blocks, 1) case A one resting on a flat surface 2) case B and the other resting on an 3) both the same (N = mg) incline. For which case is the normal force greater? 4) both the same (0 < N < mg) 5) both the same (N = 0) In Case A, we know that N = W. A y In Case B, due to the angle of B the incline, N < W. In fact, we N x f can see that N = W cos(q). q Wy W q A ConcepTest 4.12 Climbing the Rope 1) this slows your initial velocity, When you climb up a which is already upward 2) you don’t go up, you’re too heavy rope, the first thing 3) you’re not really pulling down – it just seems that way you do is pull down 4) the rope actually pulls you up on the rope. How do 5) you are pulling the ceiling down you manage to go up the rope by doing that?? ConcepTest 4.12 Climbing the Rope When you climb up a 1) this slows your initial velocity, which is already upward rope, the first thing you 2) you don’t go up, you’re too heavy do is pull down on the 3) you’re not really pulling down – it just seems that way rope. How do you 4) the rope actually pulls you up manage to go up the 5) you are pulling the ceiling down rope by doing that?? When you pull down on the rope, the rope pulls up on you!! It is actually this upward force by the rope that makes you move up! This is the “reaction” force (by the reaction rope on you) to the force that you exerted on the rope. you rope And voilá, this is Newton’s Third Law. ConcepTest 4.14a Collision Course I 1) the car A small car 2) the truck 3) both the same collides with a 4) it depends on the velocity of each large truck. 5) it depends on the mass of each Which experiences the greater impact force? ConcepTest 4.14a Collision Course I A small car collides 1) the car 2) the truck with a large truck. 3) both the same Which experiences 4) it depends on the velocity of each the greater impact 5) it depends on the mass of each force? According to Newton’s Third Law, both vehicles experience the same magnitude of force. ConcepTest 4.14b Collision Course II 1) the car In the collision 2) the truck between the 3) both the same 4) it depends on the velocity of each car and the 5) it depends on the mass of each truck, which has the greater acceleration? ConcepTest 4.14b Collision Course II 1) the car In the collision 2) the truck between the car and 3) both the same the truck, which has 4) it depends on the velocity of each the greater 5) it depends on the mass of each acceleration? We have seen that both vehicles experience the same magnitude of force. But the acceleration is given by F/m so the car has the larger acceleration, acceleration since it has the smaller mass. mass ConcepTest 4.21 Going Sledding Your little sister 1) pushing her from behind wants you to give 2) pulling her from the front 3) both are equivalent her a ride on her 4) it is impossible to move the sled sled. On level 5) tell her to get out and walk ground, what is the easiest way to accomplish this? 1 2 ConcepTest 4.21 Going Sledding Your little sister wants 1) pushing her from behind you to give her a ride 2) pulling her from the front on her sled. On level 3) both are equivalent ground, what is the 4) it is impossible to move the sled easiest way to 5) tell her to get out and walk accomplish this? In Case 1, the force F is pushing down (in addition to mg), so the normal force is larger. In Case 2, the force F larger 1 is pulling up, against gravity, so the up normal force is lessened. Recall that lessened the frictional force is proportional to the normal force. 2 ConcepTest 4.22 Will it Budge? A box of weight 1) moves to the left 100 N is at rest on 2) moves to the right a floor where ms = 3) moves up 4) moves down 0.5. A rope is 5) the box does not move attached to the box and pulled Static friction horizontally with (ms = 0.4 ) m T tension T = 30 N. Which way does the box move? ConcepTest 4.22 Will it Budge? A box of weight 100 N is at rest 1) moves to the left on a floor where ms = 0.5. A 2) moves to the right rope is attached to the box and 3) moves up pulled horizontally with 4) moves down tension T = 30 N. Which way 5) the box does not move does the box move? The static friction force has a maximum of msN = 40 N. The N Static friction T tension in the rope is only 30 N. N (ms = 0.4 ) m So the pulling force is not big enough to overcome friction. Follow-up: What happens if the tension is 35 N? What about 45 N? ConcepTest 4.23a Sliding Down I 1) component of the gravity force A box sits on a flat parallel to the plane increased board. You lift one 2) coeff. of static friction decreased end of the board, 3) normal force exerted by the board decreased making an angle with 4) both #1 and #3 the floor. As you 5) all of #1, #2 and #3 increase the angle, the box will eventually begin to Normal slide down. Why? Net Force Weight ConcepTest 4.23a Sliding Down I A box sits on a flat board. 1) component of the gravity force You lift one end of the parallel to the plane increased board, making an angle 2) coeff. of static friction decreased with the floor. As you 3) normal force exerted by the board increase the angle, the box decreased will eventually begin to 4) both #1 and #3 slide down. Why? 5) all of #1, #2 and #3 l As the angle increases, the component of weight parallel to the plane increases and the component perpendicular to the plane decreases (and so does the normal Normal force). Since friction depends on normal force, we see that the friction force gets Net Force smaller and the force pulling the box Weight down the plane gets bigger. bigger ConcepTest 5.1 To Work or Not to Work Is it possible to do work on an 1) yes object that remains at rest? 2) no ConcepTest 5.1 To Work or Not to Work Is it possible to do work on an 1) yes object that remains at rest? 2) no Work requires that a force acts over a distance. distance If an object does not move at all, there is no displacement, and therefore no work done. displacement done ConcepTest 5.2a Friction and Work I A box is being 1) friction does no work at all pulled across a 2) friction does negative work rough floor at a 3) friction does positive work constant speed. What can you say about the work done by friction? ConcepTest 5.2a Friction and Work I A box is being pulled across a rough floor at a 1) friction does no work at all 2) friction does negative work constant speed. What 3) friction does positive work can you say about the work done by friction? Friction acts in the opposite N displacement direction to the displacement, so f Pull the work is negative. Or using the negative definition of work (W = F d cos q ), since 180o, then W < 0. = mg ConcepTest 5.2b Friction and Work II Can friction ever 1) yes do positive work? 2) no ConcepTest 5.2b Friction and Work II Can friction ever 1) yes do positive work? 2) no Consider the case of a box on the back of a pickup truck. If the box moves along with the truck, then it is actually truck the force of friction that is making the box move. move ConcepTest 5.2c Play Ball! In a baseball game, the catcher stops a 90-mph 1) catcher has done positive work pitch. What can you say 2) catcher has done negative work about the work done by 3) catcher has done zero work the catcher on the ball? ConcepTest 5.2c Play Ball! In a baseball game, the catcher stops a 90-mph 1) catcher has done positive work pitch. What can you say 2) catcher has done negative work about the work done by 3) catcher has done zero work the catcher on the ball? The force exerted by the catcher is opposite in direction to the displacement of the ball, so the work is negative. Or using the negative definition of work (W = F d cos q ), since 180o, then W < 0. = Note that because the work done on the ball is negative, its speed decreases. Follow-up: What about the work done by the ball on the catcher? ConcepTest 5.2d Tension and Work A ball tied to a 1) tension does no work at all string is being 2) tension does negative work whirled around in 3) tension does positive work a circle. What can you say about the work done by tension? ConcepTest 5.2d Tension and Work A ball tied to a string is being whirled around in 1) tension does no work at all a circle. What can you 2) tension does negative work say about the work done 3) tension does positive work by tension? No work is done because the force acts in a perpendicular direction to the displacement. Or using the definition of work (W = F d cos q ), T since 180o, then W < 0. = v Follow-up: Is there a force in the direction of the velocity? ConcepTest 5.3 Force and Work 1) one force A box is being pulled 2) two forces up a rough incline by a 3) three forces rope connected to a 4) four forces 5) no forces are doing work pulley. How many forces are doing work on the box? ConcepTest 5.3 Force and Work A box is being pulled up a 1) one force rough incline by a rope 2) two forces connected to a pulley. 3) three forces 4) four forces How many forces are 5) no forces are doing work doing work on the box? dis p lac Any force not perpendicular em en to the motion will do work: t N T N does no work T does positive work f f does negative work mg does negative work mg ConcepTest 5.8a Slowing Down If a car traveling 60 1) 20 m km/hr can brake to a 2) 30 m 3) 40 m stop within 20 m, 4) 60 m what is its stopping 5) 80 m distance if it is traveling 120 km/hr? Assume that the braking force is the same in both cases. ConcepTest 5.8a Slowing Down If a car traveling 60 km/hr can 1) 20 m brake to a stop within 20 m, 2) 30 m what is its stopping distance if 3) 40 m it is traveling 120 km/hr? 4) 60 m Assume that the braking force 5) 80 m is the same in both cases. F d = Wnet = DKE = 0 – 1/2 mv2 thus: |F| d = 1/2 mv2 Therefore, if the speed doubles, doubles the stopping distance gets four times larger. larger ConcepTest 5.13 Up the Hill 1) the same Two paths lead to the top 2) twice as much of a big hill. One is steep 3) four times as much and direct, while the 4) half as much 5) you gain no PE in either other is twice as long but case less steep. How much more potential energy would you gain if you take the longer path? ConcepTest 5.13 Up the Hill Two paths lead to the top of a big 1) the same hill. One is steep and direct, while 2) twice as much the other is twice as long but less 3) four times as much steep. How much more potential 4) half as much energy would you gain if you take 5) you gain no PE in either the longer path? case Since your vertical position (height) changes by the same amount in each case, the gain in potential energy is the same. Follow-up: How much more work do you do in taking the steeper path? Follow-up: Which path would you rather take? Why? ConcepTest 5.16 Down the Hill Three balls of equal mass start from rest and roll down different ramps. All ramps have the same height. Which ball has the greater speed at the bottom of its ramp? 4) same speed for all balls 1 2 3 ConcepTest 5.16 Down the Hill Three balls of equal mass start from rest and roll down different ramps. All ramps have the same height. Which ball has the greater speed at the bottom of its ramp? 4) same speed for all balls 1 2 3 All of the balls have the same initial gravitational PE, PE since they are all at the same height (PE = mgh). Thus, when they get to the bottom, they all have the same final KE, and hence the same speed (KE = 1/2 mv2). KE Follow-up: Which ball takes longer to get down the ramp? ConcepTest 5.18a Water Slide I Paul and Kathleen start from rest at 1) Paul the same time on frictionless water 2) Kathleen slides with different shapes. At the 3) both the same bottom, whose velocity is greater? Conservation of Energy: Ei = mgH = Ef = 1/2 mv2 therefore: gH = 1/2 v2 Since they both start from the same height, they have the height same velocity at the bottom. ConcepTest 5.18b Water Slide II 1) Paul Paul and Kathleen 2) Kathleen start from rest at 3) both the same the same time on frictionless water slides with different shapes. Who makes it to the bottom first? ConcepTest 5.18b Water Slide II Paul and Kathleen start from 1) Paul rest at the same time on 2) Kathleen 3) both the same frictionless water slides with different shapes. Who makes it to the bottom first? Even though they both have the same final velocity, Kathleen is at a lower height than Paul for most of her ride. ride Thus she always has a larger velocity during her ride and therefore arrives earlier! ConcepTest 5.21a Time for Work I Mike applied 10 N of 1) Mike 2) Joe force over 3 m in 10 3) both did the same work seconds. Joe applied the same force over the same distance in 1 minute. Who did more work? ConcepTest 5.21a Time for Work I Mike applied 10 N 1) Mike of force over 3 m 2) Joe 3) both did the same work in 10 seconds. Joe applied the same force over the same Both exerted the same force over the same distance in 1 displacement. Therefore, both did the same displacement minute. Who did amount of work. Time does not matter for work determining the work done. done more work? ConcepTest 5.21b Time for Work II 1) Mike produced more power Mike performed 5 J of work in 10 secs. Joe did 3 J of work 2) Joe produced more power in 5 secs. Who produced the 3) both produced the same greater power? amount of power ConcepTest 5.21b Time for Work II 1) Mike produced more power Mike performed 5 J of work in 10 secs. Joe did 3 J of work 2) Joe produced more power in 5 secs. Who produced the 3) both produced the same greater power? amount of power Since power = work / time, we see that Mike produced 0.5 W and Joe produced 0.6 W of power. Thus, even though Mike did more work, he required twice the time to do the work, and therefore his power output was lower. ConcepTest 5.22b Energy Consumption Which contributes 1) hair dryer more to the cost of 2) microwave oven 3) both contribute equally your electric bill each 4) depends upon what you month, a 1500-Watt cook in the oven 5) depends upon how long hair dryer or a 600- each one is on 600 W Watt microwave oven? 1500 W ConcepTest 5.22b Energy Consumption 1) hair dryer Which contributes more to 2) microwave oven the cost of your electric bill 3) both contribute equally each month, a 1500-Watt 4) depends upon what you cook in the oven hair dryer or a 600-Watt 5) depends upon how long each one is on microwave oven? We already saw that what you actually pay for 600 W is energy. To find the energy consumption of energy an appliance, you must know more than just the power rating—you have to know how long it was running. running 1500 W ConcepTest 6.3a Momentum and Force A net force of 200 N acts on a 100-kg boulder, and a force of the same 1) greater than magnitude acts on a 130-g pebble. 2) less than How does the rate of change of the 3) equal to boulder’s momentum compare to the rate of change of the pebble’s momentum? ConcepTest 6.3a Momentum and Force A net force of 200 N acts on a 100-kg boulder, and a force of the same 1) greater than magnitude acts on a 130-g pebble. 2) less than How does the rate of change of the 3) equal to boulder’s momentum compare to the rate of change of the pebble’s momentum? The rate of change of momentum is, in fact, the force. Remember that F = Dp/Dt. Since the force exerted on the boulder and the pebble is the same, then the rate of change of momentum is the same. ConcepTest 6.3b Velocity and Force A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble. 1) greater than How does the rate of change of the 2) less than boulder’s velocity compare to the 3) equal to rate of change of the pebble’s velocity? ConcepTest 6.3b Velocity and Force A net force of 200 N acts on a 100 kg boulder, and a force of the same magnitude acts on a 130-g pebble. 1) greater than How does the rate of change of the 2) less than boulder’s velocity compare to the 3) equal to rate of change of the pebble’s velocity? The rate of change of velocity is the acceleration. Remember that a = Dv/Dt. The acceleration is related to the force by Newton’s 2nd Law (F = ma), so the acceleration of the boulder is less than that of the pebble (for the same applied force) because the boulder is much more massive. ConcepTest 6.4 Collision Course 1) the car A small car and a 2) the truck 3) they both have the same large truck collide momentum change head-on and stick 4) can’t tell without knowing the final velocities together. Which one has the larger momentum change? ConcepTest 6.4 Collision Course A small car and a large 1) the car truck collide head-on 2) the truck 3) they both have the same and stick together. momentum change Which one has the larger 4) can’t tell without knowing the final velocities momentum change? Since the total momentum of the system is conserved, that means that Dp = 0 for the car and truck combined. combined Therefore, Dpcar must be equal and ca opposite to that of the truck (–Dptruck) in order for the total momentum change to be zero. Note that this conclusion Follow-up: Which one feels the larger acceleration? also follows from Newton’s 3rd Law. ConcepTest 6.6 Watch Out! You drive around a curve in 1) hit the other car a narrow one-way street at 2) hit the wall 3) makes no difference 30 mph when you see an 4) call your physics identical car heading teacher! straight toward you at 30 5) get insurance! mph. You have two options: hit the car head-on or swerve into a massive concrete wall (also head-on). What should you do? ConcepTest 6.6 Watch Out! You drive around a curve in a narrow 1) hit the other car one-way street at 30 mph when you see 2) hit the wall an identical car heading straight toward 3) makes no difference you at 30 mph. You have two options: 4) call your physics hit the car head-on or swerve into a teacher! massive concrete wall (also head-on). 5) get insurance! What should you do? In both cases your momentum will decrease to zero in the collision. Given that the time Dt of the collision is the same, then the force exerted on YOU will be the same!! If a truck is approaching at 30 mph, then you’d be better off hitting the wall in that case. On the other hand, if it’s only a mosquito, well, mosquito you’d be better off running him down... down ConcepTest 6.7 Impulse A small beanbag and a bouncy rubber ball are dropped from the 1) the beanbag same height above the floor. 2) the rubber ball They both have the same mass. Which one will impart the greater 3) both the same impulse to the floor when it hits? ConcepTest 6.7 Impulse A small beanbag and a bouncy rubber ball are dropped from the 1) the beanbag same height above the floor. 2) the rubber ball They both have the same mass. Which one will impart the greater 3) both the same impulse to the floor when it hits? Both objects reach the same speed at the floor. However, while the beanbag comes to rest on the floor, the ball bounces back up with nearly the same speed as it hit. Thus, the change in momentum for the ball is greater, because of the rebound. rebound The impulse delivered by the ball is twice that of the beanbag. For the beanbag: Dp = pf – pi = 0 – (–mv ) = mv For the rubber ball: Dp = pf – pi = mv – (–mv ) = 2mv Follow-up: Which one imparts the larger force to the floor? ConcepTest 6.9a Going Bowling I A bowling ball and a ping-pong ball are 1) the bowling ball 2) same time for both rolling toward you 3) the ping-pong ball with the same 4) impossible to say momentum. If you exert the same force to stop each one, p which takes a longer time to bring to rest? p ConcepTest 6.9a Going Bowling I A bowling ball and a ping-pong ball are rolling toward you with 1) the bowling ball the same momentum. If you 2) same time for both exert the same force to stop each 3) the ping-pong ball one, which takes a longer time to 4) impossible to say bring to rest? Dp We know: Fav = so Dp = Fav Dt Dt p Here, F and Dp are the same for both balls! It will take the same amount of time to stop them. p ConcepTest 6.9b A bowling ball and a Going Bowling II ping-pong ball are 1) the bowling ball 2) same distance for both rolling toward you 3) the ping-pong ball with the same 4) impossible to say momentum. If you exert the same force to stop each one, for p which is the stopping distance greater? p ConcepTest 6.9b Going Bowling II A bowling ball and a ping-pong 1) the bowling ball ball are rolling toward you with 2) same distance for both the same momentum. If you exert 3) the ping-pong ball the same force to stop each one, 4) impossible to say for which is the stopping distance greater? Use the work-energy theorem: W = DKE. KE The ball with less mass has the greater speed (why?), and thus the greater KE (why (why?) p again?). In order to remove that KE, work again?) must be done, where W = Fd. Since the Fd p force is the same in both cases, the distance needed to stop the less massive ball must be bigger. bigger ConcepTest 6.10a Elastic Collisions I Consider two elastic collisions: 1) situation 1 1) a golf ball with speed v hits a 2) situation 2 stationary bowling ball head-on. 3) both the same 2) a bowling ball with speed v hits a stationary golf ball head-on. In which case does the golf ball have the greater speed after the collision? at rest v at rest v 1 2 ConcepTest 6.10a Elastic Collisions I Consider two elastic collisions: 1) a golf ball with speed v hits a 1) situation 1 stationary bowling ball head-on. 2) situation 2 2) a bowling ball with speed v hits a stationary golf ball head-on. In 3) both the same which case does the golf ball have the greater speed after the collision? Remember that the magnitude of the relative velocity has to be equal before v and after the collision! 1 In case 1 the bowling ball will almost remain at rest, and the golf ball will bounce back with speed close to v. In case 2 the bowling ball will keep going with speed close to v, hence the golf ball 2v will rebound with speed close to 2v. v 2 ConcepTest 6.10b Elastic Collisions II 1) zero Carefully place a small rubber ball 2) v (mass m) on top of a much bigger 3) 2v basketball (mass M) and drop these 4) 3v from some height h. What is the 5) 4v velocity of the smaller ball after the basketball hits the ground, reverses direction and then collides with small rubber ball? ConcepTest 6.10b Elastic Collisions II Carefully place a small rubber ball (mass m) 1) zero on top of a much bigger basketball (mass M) 2) v and drop these from some height h. What is 3) 2v the velocity of the smaller ball after the 4) 3v basketball hits the ground, reverses direction 5) 4v and then collides with small rubber ball? • Remember that relative 3v velocity has to be equal v m v before and after collision! Before the collision, the v basketball bounces up v M v with v and the rubber ball is coming down with v, (a) (b) (c) so their relative velocity is –2v. After the collision, it Follow-up: With initial drop height h, how –2v therefore has to be +2v!! +2v high does the small rubber ball bounce up? ConcepTest 6.14b Recoil Speed II A cannon sits on a 1) 0 m/s 2) 0.5 m/s to the right stationary railroad 3) 1 m/s to the right flatcar with a total 4) 20 m/s to the right mass of 1000 kg. 5) 50 m/s to the right When a 10-kg cannon ball is fired to the left at a speed of 50 m/s, what is the recoil speed of the flatcar? ConcepTest 6.14b Recoil Speed II A cannon sits on a stationary 1) 0 m/s railroad flatcar with a total mass of 2) 0.5 m/s to the right 1000 kg. When a 10-kg cannon ball 3) 1 m/s to the right is fired to the left at a speed of 50 4) 20 m/s to the right m/s, what is the recoil speed of the 5) 50 m/s to the right flatcar? Since the initial momentum of the system was zero, the final total momentum must also be zero. Thus, the final momenta of the cannon ball and the flatcar must be equal and opposite. pcannonball = (10 kg)(50 m/s) = 500 kg-m/s pflatcar = 500 kg-m/s = (1000 kg)(0.5 m/s) ConcepTest 6.15 Gun Control When a bullet is fired from a gun, the bullet 1) it is much sharper than the gun and the gun have equal 2) it is smaller and can penetrate your body and opposite momenta. 3) it has more kinetic energy than the gun If this is true, then why 4) it goes a longer distance and gains speed is the bullet deadly? (whereas it is safe to 5) it has more momentum than the gun hold the gun while it is fired) ConcepTest 6.15 Gun Control When a bullet is fired from a gun, the bullet 1) it is much sharper than the gun and the gun have equal 2) it is smaller and can penetrate your body and opposite momenta. 3) it has more kinetic energy than the gun If this is true, then why 4) it goes a longer distance and gains speed is the bullet deadly? (whereas it is safe to 5) it has more momentum than the gun hold the gun while it is fired) While it is true that the magnitudes of the momenta of the gun and the bullet are equal, the bullet is less massive and so it has a much higher velocity. Since KE is related to v2, the bullet has considerably more KE and therefore can do more damage on impact. ConcepTest 6.16a Crash Cars I If all three collisions 1) I 2) II below are totally 3) I and II inelastic, which one(s) 4) II and III 5) all three will bring the car on the left to a complete halt? ConcepTest 6.16a Crash Cars I If all three collisions below 1) I are totally inelastic, which 2) II 3) I and II one(s) will bring the car on 4) II and III the left to a complete halt? 5) all three In case I, the solid wall clearly stops the car. In cases II and III, since ptot = 0 before the collision, collision then ptot must also be zero after the collision, which collision means that the car comes to a halt in all three cases. ConcepTest 6.16b Crash Cars II 1) I 2) II If all three collisions 3) III below are totally 4) II and III inelastic, which 5) all three one(s) will cause the most damage (in terms of lost energy)? ConcepTest 6.16b Crash Cars II 1) I If all three collisions below are 2) II totally inelastic, which one(s) 3) III will cause the most damage 4) II and III (in terms of lost energy)? 5) all three The car on the left loses the same KE in all 3 cases, but in case III, the car on III the right loses the most KE because KE = 1/2 m v2 and the car in case III has the largest velocity. velocity ConcepTest 6.17 Shut the Door! You are lying in bed and 1) the superball you want to shut your 2) the blob of clay 3) it doesn’t matter -- they bedroom door. You have a will be equally effective superball and a blob of clay 4) you are just too lazy to (both with the same mass) throw anything sitting next to you. Which one would be more effective to throw at your door to close it? ConcepTest 6.17 Shut the Door! You are lying in bed and you want to 1) the superball shut your bedroom door. You have a 2) the blob of clay superball and a blob of clay (both 3) it doesn’t matter -- they with the same mass) sitting next to will be equally effective you. Which one would be more 4) you are just too lazy to throw anything effective to throw at your door to close it? The superball bounces off the door with almost no loss of speed, so its Dp (and that of the door) is 2mv. mv The clay sticks to the door and continues to move along with it, so its Dp is less than that of the superball, and therefore it superball imparts less Dp to the door.

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