Newton’s First Law • An object at rest will remain at rest and an object in motion will remain in motion unless acted on by an outside net force. Newton’s Second Law • The net force acting on an object equals the object’s mass multiplied by its acceleration. • F = ma • a.k.a. an object’s acceleration is inversely proportional to it’s mass and directly proportional to the force applied What Changes? • Almost nothing changes • We now have a few more types of problems. Constant Velocity/Rest • Some objects are still at rest or moving at a constant velocity. • The acceleration of these objects is zero, thus ma = 0 • Therefore the net force in both directions is zero. Find Acceleration • You are given all of the forces acting on an object and you have to find the acceleration of the object. • Find the net force in both directions and set that equal to ma. Find a. Red Wagon • You are pulling a small child down the street in a wagon. The wagon and the child have a combined mass of 48 kg. You are pulling to the right with a force of 120 N. There is a frictional force of 74 N opposing the motion. Find the resulting acceleration of the wagon. Could You Get That? • You’re going to pick a 3.5 kg bag up off of the floor. You are pulling up with a force of 37 N. What is the acceleration of the bag after it has left the ground? Atwood Machine • You have two masses suspended over a pulley as shown. Assuming the pulley to massless and frictionless find the acceleration of the two blocks. 4 kg 3 kg Moving In • Two people are pulling a 32 kg couch up to their second floor apartment. One person pulls with a force of 177 N at an angle of 55o above the horizontal while the other person pull with a force of 203 N at an angle of 60o with the opposite horizontal. Find the acceleration of the couch after it leaves the ground. Find Some Force • You are given the acceleration of an object and now you have to find what forces are causing this. • You often have to find one particular force that is acting on the object. Sledding Season • You are sledding down a hill that is inclined at 18o. You and your sled have a combined mass of 75 kg and you travel down the hill with an acceleration of 2.3 m/s2. What is the force of friction slowing down your trip? Rolling On The Table • A cart is on a table as shown. Find the acceleration of the car assuming no friction. 875 g 85 g Big Boat • A supertanker (mass = 1.70 x 108 kg) is moving with a constant velocity. Its engines generate a forward thrust of 7.4 x 105 N. Determine the magnitude of the resistive force exerted on the tanker by the water and the magnitude of the upward buoyant force exerted on the tanker by the water. Ramps and Blocks • A frictionless car is sitting on the ramp as shown. What is the acceleration of the system? 0.6 kg 32o Remember Kinematics • You are usually looking for either a force or a kinematics quantity. • You are given enough information to find acceleration by using F = ma or using kinematics. • Find a and use it to find what you are looking for. I’m Not A Good Skier • An 83 kg skier starts from rest and skis down a hill with an angle of 30o. The kinetic friction between himself and the ground is 75 N. Given that the hill is 100 m long find his final velocity and time when he reaches the bottom of the hill. • T = 7.07 seconds • Vf = 28.3 m/s Hallway Bowling Turk is bowling a patient down a hallway of Sacred Heart Hospital. What force did Turk have to exert on the 78 kg wheel chair in order to get it going from 2.8 m/s to 3.5 m/s in 0.5 seconds. After Turk let go of the wheel chair it slowed down due to friction (in the wheels) to a speed of 3.0 m/s over the 15 m long hallway to the “pins”. Find what average force the “pins” had to exert on the wheel chair to get it to stop in 1.2 seconds? (Remember that friction is constant until the chair stops.) Answers: Fpush = 117.65 N FF = -8.45 N Fpins = -186.55 N It’s A Bird… • The Superman roller coaster uses powerful magnets to accelerate a car and its riders from rest to 45 m/s (about 100 mph) in a time of 7.0 sec. The mass of the car and the riders is 5.5 x 103 kg. Find the average net force exerted on the car and the riders. • F = 35357 N Throw Up • A boy throws a steel ball straight up. Consider the motion of the ball only after it has left the boy’s hand but before it touches the ground, and assume that the forces exerted by the air are negligible. For these conditions, the force(s) acting on the ball is (are): A. A downward force of gravity along with a steadily decreasing upward force. B. A steadily decreasing upward force from the moment it leaves the boy’s hand until it reaches its highest point; on the way down there is a steadily increasing downward force of gravity as the object gets closer to the earth. C. An almost constant downward force of gravity along with an upward force that steadily decreases until the ball reaches its highest point; on the way down there is only a constant downward force of gravity D. A constant downward force of gravity only. E. None of the above. The ball falls back to the ground because of its natural tendency to rest on the surface of the earth. Bang • A 15 g bullet is fired from a rifle. It takes 2.50 x 10-3 s for the bullet to travel the length of the barrel, and it exits the barrel with a speed of 715 m/s. Assuming that the acceleration of the bullet is constant, find the average net force exerted on the bullet. • F = 4290 N Could MJ Be More Useless? Spider-Man has to save the day again, but can he? How strong must his web be? At one point the Green Goblin hits Spider-Man making him lose his grip on the cable. We can assume that the cable and car with people has a weight of around ?????? N. Now if Spider-Man lost his grip on the car for ?#? seconds what force must Spider-Man and his web hold to return the car to rest in ?#? seconds? Don’t Forget • The following mass is hung via ropes. Find the tensions in each of the ropes 35o 16 kg Friction • Friction (FF) is the force that opposes motion between 2 surfaces in contact. • There are two types of friction. Static Friction • The friction force that exists between two objects that are NOT in motion relative to one another. • Example: Try pushing a school bus that’s in park. Guess why it isn’t moving. Kinetic Friction • A.K.A. Sliding Friction • The friction force between two objects that ARE in motion relative to one another. • Example: Slide your desk along the floor. The resistance is kinetic friction. Finding Friction • Friction is found by multiplying the coefficient of friction by the normal force • FF = mN • Or FF = mFN What Is m? • The coefficient of friction (m) is a constant value based on the surfaces in contact. • It is a pure number (no unit) Will It Move? • A block whose weight is 45.0 N rests on a horizontal table. A horizontal force of 36.0 N is applied to the block. The coefficients of static and kinetic friction are 0.650 and 0.420, respectively. Will the block move under the influence of the force, and, if so, what will be the block’s acceleration? Slide It Again • If you use a horizontal force of 30.0 N to slide a 12.0 kg wooden crate across a floor at a constant velocity, what is the coefficient of sliding friction between the crate and the floor? • A rock is thrown straight up from the earth's surface. Which one of the following statements concerning the net force acting on the rock at the top of its path is true? a) The net force is equal to the weight of the rock. b) The net force is instantaneously equal to zero newtons. c) The net force’s direction changes from up to down. d) The net force is greater than the weight of the rock. e) The net force is less than the weight of the rock, but greater than zero newtons. I Love This Movie An EMP took out the power of the ship Serenity. The pilot must coast the ship to a landing. If the runway that they landed on was 500 m long and they were coming in at 42 m/s what was the coefficient of friction between Serenity and the ground? (Assume Earth gravity) Ramps and Friction • A block is at rest before sliding down the ramp as shown. Find how far the block will slide down the ramp after 4 seconds if m = 0.28. 32o Ramps and Friction II • Assuming each surface has a coefficient of friction with the blocks of 0.36 find how far the system will be displaced after 5.0 seconds. 3 kg 23o 34o Box Glide • A woman exerts a constant force on a large box. As a result, the box moves across a horizontal floor at a constant speed “v”. The constant horizontal force applied by the woman: A. Has the same magnitude as the weight of the box. B. Is greater than the weight of the box. C. Has the same magnitude as the total force which resists the motion of the box D. Is greater than the total force which resists the motion of the box. E. Is greater than either the weight of the box or the total force which resists its motion Box Glide II • If the woman in the previous question doubles the constant horizontal force that she exerts on the box to push it on the same horizontal floor, the box then moves: A. With a constant speed that is double the speed “v” in the previous question. B. With a constant speed that is greater than the speed “v” in the previous question, but not necessarily twice as great. C. For a while with a speed that is constant and greater than the speed “v” in the previous question, then with a speed that increases thereafter. D. For a while with an increasing speed, then with a constant speed thereafter. E. With a continuously increasing speed Box Glide III • If the woman in the previous questions suddenly stops applying a horizontal force to the block, then the block will: A. Immediately come to a stop. B. Continue moving at a constant speed for a while and then slow to a stop. C. Continue at a constant speed. D. Immediately start slowing to a stop. E. Increase its speed for a while and then start slowing to a stop. I Saw This Movie 11 Times In The Theater Neo kicks Agent Smith in the chest and sends him flying back through the hallway. If Agent Smith hits the ground with a velocity of ??? m/s away from Neo how far should he have slid after he made contact with the ground assuming the standard coefficient of friction between clothing and a wooden floor of 0.3? • The wheels of an automobile are locked as it slides to a stop from an initial speed of 30.0 m/s. If the coefficient of kinetic friction is 0.600 and the road is horizontal, approximately how long does it take the car to stop? A. 4.22 s B. 8.75 s C. 15.3 s D. 5.10 s E. 10.4 s Newton’s Third Law • For every action there is an equal and opposite reaction. Equal in magnitude and opposite in direction. • Forces occur in pairs. You Can Always Say… • If you push on the wall with 10 N of force, • Then the wall pushes on you with 10 N of force. • If your book pushes down on your desk with 7 N of force, • Then your desk pushes up on your book with 7 N of force. • If Object A pushes on Object B, • Then Object B pushes back equally and in the opposite direction on Object A Newton’s Apple • Isaac Newton once saw on apple fall from a tree. He realized that the force of gravity is what pulls the apple to the Earth. Now that you know Newton’s 3rd Law find the force that the apple exerts on the Earth given that the apple has a mass of 0.3 kg. Tug of War • Two students A & B are going to pull on one another via a rope in a game of tug of war. Each student is sitting on a cart with frictionless wheels. Student A has a mass of 100 kg and student B has a mass of 50 kg. Student A pulls with a force of 40 N and student B pulls with a force of 10 N. Which of the following is true: A. Student A’s acceleration is 2 times greater than student B. B. Student A’s acceleration is 4 times greater than student A. C. Student B’s acceleration is 2 times greater than student A. D. Student B’s acceleration is 4 times greater than student A. E. Student A and student B have the same acceleration. •Two identical blocks are pulled along a rough surface as suggested in the figure. Which one of the following statements is false? a) The coefficient of kinetic friction is the same in each case. b) A force of the same magnitude is needed to keep each block moving. c) A force of the same magnitude was required to start each block moving. d) The normal force exerted on the blocks by the surface is the same for both blocks. e) The magnitude of the force of kinetic friction is greater for the block on the right. Fasten Your Seatbelt • A large truck collides head on with a small compact car. During the collision: A. The truck exerts a greater amount of force on the car than the car exerts on the truck. B. The car exerts a greater amount of force on the truck than the truck exerts on the car. C. Neither exerts a force on the other, the car gets smashed simply because it gets in the way of the truck. D. The truck exerts a force on the car but the car does not exert a force on the truck. E. The truck exerts the same amount of force on the car as the car exerts on the truck.