Chapter 2 Homework 10. If the average speed of an orbiting space shuttle is 19,800 mi/h, determine the time required for it to circle earth. The shuttle orbits about 200 mi above earth and assume that earth’s radius is about 3,963 mi. 23. The engine of a model rocket accelerates the rocket vertically upward for 2.0s as follows: At t=0, the rocket’s speed is zero; at t=1.0s, its speed is 5.0 m/s; and at t=2.0s, its speed is 16 m/s. Plot a velocity vs time graph for this motion, and use the graph to determine (a) the rocket’s average acceleration during the 2.0s interval and (b) the instantaneous acceleration of the rocket at t=1.5s. 30. A truck on a straight road starts from rest and accelerates at 2.0 m/s² until it reaches a speed of 20 m/s. Then the truck travels for 20s at a constant speed until the brakes are applied, stopping the truck in a uniform manner in an additional 5.0s. (a) How long is the truck in motion? (b) What is the average velocity of the truck during the motion described? 36. A car accelerates uniformly from rest to a speed of 40 mi/h in 12.0s. Find (a) the distance the car travels during this time and (b) the constant acceleration of the car. 37. A car starts from rest and travels for 5s with a uniform acceleration of +1.5 m/s². The driver then applies the brakes, causing a uniform acceleration of -2.0 m/s². If the brakes are applied for 3.0s, (a) how fast is the car going at the end of the braking period, and (b) how far has the car gone? 43. A ball is thrown vertically upward with a speed of 25.0 m/s. (a) How high does it rise? (b) How long does it take to reach the highest point? (c) How long does the ball take to hit the ground after it reaches the highest point? (d) What is its velocity when it returns to the level from which it started? 49. A model rocket is launched straight upward with an initial speed of 50 m/s. It accelerates with a constant upward acceleration of 2 m/s until its engines stop at an altitude of 150m. (a) What is the max height reached by the rocket? (b) How long after lift off does the rocket reach its max height? (c) How long is the rocket in the air? 50. A parachutist with a camera descends in free fall at a speed of 10 m/s. The parachutist releases the camera at an altitude of 50m. (a) How long does it take the camera to reach the ground? (b) What is the velocity of the camera just before it hits the ground? 57. A ball is thrown upward from the ground with an initial speed of 25 m/s; at the same instant, another ball is dropped from a building 15m high. After how long will the balls be at the same height? 58. Two students are on a balcony 19.6m above the street. One student throws a ball vertically down at 14.7 m/s; at the same instant, the other student throws a ball vertically upward at the same speed. The second ball just misses the balcony on the way down. (a) What is the difference in the two balls’ time in the air? (b) What is the velocity of each ball as it strikes the ground? (c) How far apart are the balls .8s after they are thrown? CHAPTER 3 Chapter 3 Homework 18. The helicopter view in figure P3.18 shows two people pulling on a stubborn mule. Find (a) the single force that is equivalent to the two forces shown and (b) the force that a third person would have to exert on the mule to make the net force equal to zero. The forces are measured in units of newtons (N). 24. A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 18 m/s. The cliff is 50 m above a flat, horizontal beach, as shown below. How long after being released does the stone strike the beach below the cliff? With what speed and angle of impact does the stone land? 29. A brick is thrown upward from the top of a building at an angle of 25 degrees to the horizontal and with an initial speed of 15 m/s. If the brick is in flight for 3.0 s, how tall is the building? 31. A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 24 degrees below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 4.00 m/s² for a distance of 50.0 m to the edge of the cliff, which is 30 m above the ocean. Find (a) the cars position relative to the base of the cliff when the car lands in the ocean, and (b) the length of time the cat is in the air. 33. A projectile is launched with an initial speed of 60 m/s at an angle of 30 degrees above the horizontal. The projectile lands on a hillside 4s later. Neglect air friction. (a) what is the projectile’s velocity at the highest point of its trajectory? (b) what is the straight line distance from where the projectile was launched to where it hits its target? 49. A rocket is launched at an angle of 53 degrees above the horizontal with an initial speed of 100 m/s. The rocket moves for 3s along its initial line of motion with an acceleration of 30 m/s². At this time, its engines fail and the rocket proceeds to move as a projectile. Fine (a) the maximum altitude reached by the rocket, (b) its total time of flight, and (c) its horizontal range. 55. A home run is hit in such a way that the baseball just clears a wall 21m high, located 120 m from home plate. The ball is hit at an angle of 35 degrees to the horizontal and air resistance in negligible. Fine (a) the initial speed of the ball, (b) the time is takes the ball to reach the wall, and (c) the velocity components and the speed of the ball when it reaches the wall. (Assume that the ball is hit at a height of 1.0m above the ground.) 56. A ball is thrown straight upward and returns to the thrower’s hand after 3s in the air. A second ball is thrown at an angle of 30 degrees with the horizontal. At what speed much the second ball be thrown so that it reaches the same height as the one thrown vertically? 57. A quarterback throws a football toward a receiver with an initial speed of 20m/s at an angle of 30 degrees above the horizontal. At that instant, the receiver is 20m from the quarterback. In what direction and with what constant speed should the receiver run in order to catch the football at the level at which it was thrown? 58. A 2.00m-tall basketball player is standing on the floor 10m from the basket. If he shoots the ball at a 40 degree angle with the horizontal, at what initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? The height of Chapter 4 Homework 16. Find the tension in the two wires that support the 100 N light fixture in the figure. 20. Two people are pulling a boat through the water as in the figure. Each exerts a force of 600 N directed at a 30 degree angle relative to the forward motion of the boat. If the boat moves with constant velocity, find the resistive force exerted by the water on the boat. 26. Two packing crates of masses 10 kg and 5 kg are connected by a light string that passes over a frictionless pulley as shown in the figure. The 5 kg crate lies on a smooth incline of angle 40 degrees. Find the acceleration of the 5 kg crate and the tension in the string. 30. An object with a mass m1=5 kg rests on a frictionless horizontal table and is connected to a cable that passes over a pulley and is then fastened to a hanging object with mass m2=10 kg, as shown in the figure. Find the acceleration of each object the the tension in the cable. 34. Two objects with masses of 3 kg and 5 kg are connected by a light string that passes over a frictionless pulley, as in the figure. Determine (a) the tension in the string, (b) the acceleration of each object, and (c) the distance each object will move in the first second of motion if both objects start from rest. 41. The coefficient of static friction between the 3 kg crate and the 35 degree incline of the figure is .3. What minimum force must be applied to the crate perpendicular to the incline to prevent the crate from sliding down the incline? 49. Find the acceleration reached by each of the two objects shown in the figure if the coefficient of kinetic friction between the 7 kg object and the plane is .25. 50. A 2 kg black is held in equilibrium on an incline of angle 60 degrees by a horizontal force applied in the direction shown in the figure. If the coefficient of static friction between the block and the incline is .3, determine (a) the minimum value of the force pushing the block, and (b) the normal force exerted by the incline on the block. 55. What is the resultant force exerted by the 2 cables supporting the traffic light in the figure? What is the weight of the light? 58. (a) What is the minimum force of friction required to hold the system if the figure in equilibrium? (b) What coefficient of static friction between the 100N block and the table ensures equilibrium? (c) If the coefficient of kinetic friction between the 100N block and the table is .25, what hanging weight should replace the 50 N weight to allow the system to move at a constant speed one it is set in motion? Chapter 5 Homework 13. A 70-kg base runner begins his slide into second base when he is moving at a speed of 4 m/s. The coefficient of friction between his clothes and the earth is .70. He slides so that his speed is zero just as he reaches the base. (a) how much mechanical energy is lost due to friction acting on the runner? (b) How far does he slide? 15. A 2-kg bullet leaves the barrel of a gun at a speed of 300 m/s. (a) Find its kinetic energy. (b) Find the average force exerted by the expanding gases on the bullet as it moves the length of the 50 cm long barrel. 17. A 2000 kg car moves down a level highway under the actions of two forces: a 1000 N forward force exerted on the drive wheels by the road and a 950 N resistive force. Use the work energy theorem to find the speed of the car after it has moved a distance of 20m, assuming that it starts from rest. 25. The chin up is one exercise that can be used to strengthen the biceps muscle. This muscle can exert a force approximately 800N as it contracts a distance of 7.5cm in a 75kg male. How much work can the biceps muscles (one in each arm) perform in a single contraction? Compare this amount of work with the energy required to life a 75kg person 40cm in performing a chin up. Do you think the biceps muscle is the only muscle involved in performing a chin up? 28. A .400 kg bead slides on a curved wire, starting from rest at point A. If the wire is frictionless, find the speed of the bead at B and C. 32. Three objects with masses M1=5kg, M2=10kg, and M3=15kg, respectively, are attached by strings over frictionless pulleys. The horizontal surface is frictionless and the system is released from rest. Using energy concepts, find the speed of M3 after it moves down a distance of 4.0m. 33. The launching mechanism of a toy gun consists of a spring of unknown spring constant. If the spring is compressed a distance of .120m and the gun fired vertically, the gun can launch a 20g projectile from rest to a max height of 20m above the starting point of the projectile. Neglecting all resistance of forces, determine (a) the spring constant, and (b) the speed of the projectile as it moves through the equilibrium position of the spring (where x=0). 42. A 25 kg child on a 2m long swing is released from rest when the ropes of the swing make an angle of 30 degrees with the vertical. (a) neglecting friction, find the child’s speed at the lowest position. (b) If the actual speed of the child at the lowest point is 2m/s, what is the mechanical energy lost due to friction? 63. Two objects are connected by a light string passing over a light, frictionless pulley. The 5 kg object is released from rest at a point 4m above the floor. (a) Determine the speed of each object at the moment the 5kg object hits the floor. (b) How much higher does the 3kg object travel after the 5kg object hits the floor? 64. Two blocks, A and B (with mass 50kg and 100kg respectively) are connected by a string. The pulley is frictionless and of negligible mass. The coefficient of kinetic friction between Block A and the incline is .25. Determine the change in the kinetic energy of block A as it moves from C to D, a distance of 20m up the incline if the system starts from rest. 31. Tarzan swings on a 30m vine initially inclined at an angle of 37 degrees with the vertical. What is his speed at the bottom of the swing (a) if he starts from rest? (b) If he pushes off Chapter 6 Homework 15. The front 1.20m of a 1400kg car is designed as a “crumple zone” that collapses to absorb the shock of a collision. If a car traveling 25m/s stops uniformly in 1.2m (a) how long does the collision last, (b) what is the magnitude of the average force on the car, (c) what ids the acceleration of the car? Express the acceleration as a multiple of the acceleration of gravity. 22. A 65kg person throws a .045 0-kg snowball forward with a ground speed of 30m/s. a second person, with a mass of 60 kg catches the snowball. Both people are on skates. The first person is initially moving forward at a speed of 2.5 m/s, and the second person is initially at rest. What are the velocities of the two people after the snowball is exchanged? Disregard friction between skates and the ice. 28. A 7g bullet is fired into a 1.5kg ballistic pendulum. The bullet emerges from the block with a speed of 200 m/s, and the block rises to a maximum height of 12cm. Find the initial speed of the bullet? 30. An 8g bullet is fired into a 250g block that is initially at rest at the edge of a table with a height of 1m. The bullet remains in the block, and after the impact the block lands 2m from the bottom of the table. Determine the initial speed of the bullet. 35. A 5g object moving to the right at 20cm/s makes an elastic head on collision with a 10g object that is initially at rest. Find (a) the velocity of each object after the collision and (b) the fraction of the initial kinetic energy transferred to the 10g object. 52. A .4kg green bead slides on a curved frictionless wire, starting from rest at Point A. At Point B, the bead collides elastically with a .6kg blue ball at rest. Find the maximum height the blue ball rises as it moves up the wire. 56. Two blocks of masses m1 = 2 kg and m2= 4kg are each released from rest at a height of 5m on a frictionless track, and undergo an elastic head on collision (a) determine the velocity of each block just before the collision and (b) determine the velocity of each block immediately after the collision and (c) determine the maximum heights to which m1 and m2 rise after the collision. 57. A .5kg block is released from rest at the top of a frictionless track 2.5m above the top of the table. It them collides elastically with a 1kg object that is initially at rest on the table. (a) Determine the velocities of the two objects just after the collision. (b) How high up the track does the .5 kg object travel back after the collision? (c) How far away from the bottom of the table does the 1kg object land, given that the table is 2m high? (d) How far away from the bottom of the table does the .5kg object eventually land? 59. A small block of mass m1= .5kg is released from rest from the top of a curved wedge of mass m2=3kg, which sits on a frictionless horizontal surface. When the block leaves the wedge, its velocity is measured to be 4m/s to the right. (a) what is the velocity of the wedge after the block reaches the horizontal surface? (b) What is the height h of the wedge? 60. Two carts of equal mass m= .25kg are placed on a frictionless track that has a light spring of force constant k= 50N/m attached to one end of it. The red cart is given an initial velocity of 3m/s to the right and the blue cart is initially at rest. If the carts collide elastically find (a0 the velocity of the carts just after the first collision and (b) the maximum compression of the spring. Chapter 7 Homework 7. A machine part rotates at an angular speed of 60rad/s; its speed is then increased to 2.2 rad/s at am angular acceleration of .7rad/s². Find the angle through which the part rotates before reaching this final speed. 17. (a) What is the tangential acceleration of a bug on the rim of a 10in diameter disk if the disk moves from rest to an angular speed of 78 rev/min in 3s? (b) When the disk is at its final speed, what is the tangential velocity of the bug? (c) One second after the bug starts from rest, what are its tangential acceleration, centripetal acceleration, and total acceleration? 18. A race car starts from rest on a circular track of radium 400m. The car’s speed increases at a constant rate of .5m/s². At the point where the magnitudes of the centripetal and tangential accelerations are equal, determine (a) the speed of the race car, (b) the distance traveled, and (c) the elapsed time. 23. A 50 kg child stands at the rim of a merry go round of radius 2m, rotating with an angular speed of 3rad/s. (a) What is the child’s centripetal acceleration? (b) What is the minimum force between the feet and the floor of the carousel that is required to keep the child in a circular path? (c) What minimum coefficient of static friction is required? Is the answer you found reasonable? In other words is she likely to stay on the merry go round? 26. Tarzan (m=85kg) tries to cross a river by swinging from a 10m long vine. His speed at the bottom of the swing (as he just clears the water) is 8m/s. Tarzan doesn’t know that the vine has a breaking strength of 1000N. Does he make it safely across the river? Justify your answer. 27. A 40kg child takes a ride on a ferris wheel that rotates 4 times each minute and has a diameter of 18m. (A) what is the centripetal acceleration of the child? (B) What force (magnitude and direction) does the seat exert on the child at the lowest point of the ride? (C) What force does the seat exert on the child at the highest point of the ride? (D) What force does the seat exert on the child when the child is halfway between the top and the bottom? 28. A roller coaster vehicle has a mass of 500kg when fully loaded with passengers. (A) if the vehicle has a speed of 20m/s at point A, what is the force of the track on the vehicle at this point? (B) What is the maximum speed the vehicle can have at point B in order for gravity to hold it on the track? 48. A .4kg pendulum bob passes through the lowest part of its path at a speed of 3m/s. (A) what is the tension in the pendulum cable at this point if the pendulum is 80 cm long? (B) When the pendulum reaches its highest point, what angle does the cable make with the vertical? (C) What Chapter 8 Homework 2. A steel band exerts a horizontal force of 80N on a tooth at point B. What is the torque on the root of the tooth about point A? 33. A cylindrical fishing reel has a moment of inertia I=6.8x10^-4 kgm² and a radius of 4cm. A friction clutch in the reel exerts a restraining torque of 1.3Nm if a fish pulls on the line. The fisherman gets a bite, and the reel begins to spin at an angular acceleration of 66rad/s². (A) What is the force exerted by the fish on the line? (B) How much line unwinds in .5s? 36. A 5kg cylindrical reel with a radius of .6m and a frictionless axle start from rest and speeds up uniformly as a 3kg bucket falls into a well, making a light rope unwind from the reel. The bucket starts from rest and falls for 4s. (A) What is the linear acceleration of the falling bucket? (B) How far does it drop? (C) What is the angular acceleration of the reel? 37. An airliner lands with a speed of 50m/s. Each wheel of the plane has a radius of 1.25 m and a moment of inertia of 110 kgm². At touchdown, the wheels begin to spin under the action of friction. Each wheel supports a weight of 1.4x10^4N, and the wheels attain their angular speed in .48s while rolling without slipping. What is the coefficient of kinetic friction between the wheels and the runway? Assume that the speed of the plane is constant. 44. A 240 N sphere .2m in radius rolls without slipping 6m down a ramp that is incline at 37 degrees with the horizontal. What is the angular speed of the sphere at the bottom of the slope if it starts from rest? 49. A solid, horizontal cylinder of mass 10 kg and radius 1m rotates with an angular speed of 7rad/s about a fixed vertical axis through its center. A .25kg piece of putty is dropped vertically onto the cylinder at a point .9m from the center of rotation and sticks to the cylinder. Determine the final angular speed of the system. 60. A 12 kg object is attached to a cord that is wrapped around a wheel of radius 10cm. The acceleration of the object down the frictionless incline is measured to be 2m/s². Assuming the axle of the wheel to be frictionless, determine (A) the tension in the rope (B) the moment of inertia of the wheel, and (C) the angular speed of the wheel 2s after it begins rotating, starting Chapter 9 Homework 24. Piston 1 in the figure has a diameter of .25 in; piston 2 has a diameter of 1.5in. In the absence of friction, determine the force necessary to support the 500-lb weight. 35. A sample of an unknown material appears to weight 300N in air and 200N when immersed in alcohol of specific gravity .7. What are (a) the volume, and (b) the density of the material? 36. An object weighing 300N in air is immersed in water after being tied to a string connected to a balance. The scale now reads 265N. Immersed in oil, the object appears to weigh 275N. Find (a) the density of the object and (b) the density of the oil. 39. A 1.00kg beaker containing 2.00kg of oil (density = 916 kg/m³) rests on a scale. A 2.00kg block of iron is suspended from a spring scale and is completely submerged in the oil. Find the equilibrium readings of both scales. 43. A hypodermic syringe contains a medicine with a density of water. The barrel of the syringe has a cross sectional area of 2.5 x 10^-5 m². In the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force of magnitude 2.00N is exerted on the plunger, making medicine squirt from the needle. Determine the medicine’s flow speed through the needle. Assume that the pressure in the needle remains equal to 1.00atm and that the syringe is horizontal. 45. A jet of water squirts out horizontally from a hole near the bottom of the take. If the hole has a diameter of 3.5 mm, what is the height of the water level in the tank? 47. The inside diameters of the larger portions of the horizontal pipe in the figure are 2.5 cm. Water flows to the right at a rate of 1.8 x 10^-4 m³/s. Determine the inside diameter of the Chapter 10 Homework 10. A cylindrical brass sleeve is to be shrink-fitted over a brass shaft whose diameter is 3.212 cm at 0 degrees Celsius. The diameter of the sleeve is 3.196 cm at 0 degrees Celsius. (a) To what temperature must the sleeve be heated before it will slip over the shaft? (b) Alternatively, to what temperature must the shaft be cooled before it will slip into the sleeve? 11. The New River George bridge in West Virginia is a 518m long steel arch. How much will its length change between temperature extremes of -20 degrees Celsius and 35 degrees Celsius? 13. A pair of eyeglass frames are made of epoxy plastic (coefficient of linear expansion = 1.20 x 10^-4 Π˚C ^-1). At room temperature (20 degrees C), the frames have circular lens holes 2.20 cm in radius. To what temperature must the frames be heated if lenses 2.21cm in radius are to be inserted into them? 15. A brass ring of diameter 10.00 cm at 20 degrees C is heated and slipped over an aluminum rod of diameter 10.01 cm at 20 degrees C. Assuming the average coefficients of linear expansion are constant, (a) to what temperature must the combination be cooled to separate the two metals? Is that temperature attainable? (b) What id the aluminum rod were 10.02 cm in diameter? 20. The Trans-Alaskan pipeline is 1300km long, reaching from Prudhoe Bay to the port of Valdez, and is subject to temperatures ranging from -73 degrees C to +35 degrees C. How much does the steel pipeline expand due to the different in temperature? How can this expansion be compensated for? 21. An automobile fuel tank is filled to the brim with 45 L (12 gal) of gasoline at 10 degrees C. Immediately after, the vehicle is parked in the sunlight, where the temperature is 35 degrees C. How much gasoline overflows from the tank as a result of the expansion? (Neglect the Chapter 11 Homework 11. A 200g aluminum cup contains 800g of water in thermal equilibrium with the cup at 80 degrees C. The combination of cup and water is cooled uniformly so that the temperature decreases by 1.5 degrees C per minute. At that rate is energy being removed? Express your answer in watts. 16. It is desired to cool iron parts from 500 degrees F to 100 degrees F by dropping them into water that is initially 75 degrees F. Assuming that all the heat from the iron is transferred to the water and that none of the water evaporated, how many kilograms of water are needed per kilogram of iron? 17. A 100g aluminum calorimeter contains 250g of water. The two substances are in thermal equilibrium at 10 degrees C. Tow metallic blocks are placed in the water. One is a 50g piece of copper at 80 degrees C. The other sample has a mass of 70g and is originally at a temperature of 100 degrees C. The entire system stabilizes at a final temperature of 20 degrees C. Determine the specific heat of the unknown second sample. 19. A student drops to metallic objects into a 120 g steel container holding 150 g of water at 25 degrees C. One object is a 200g cube of copper that is initially at 85 degrees C, and the other is a chunk of aluminum that is initially at 5 degrees C. To the surprise of the student, the water reaches a final temperature of 25 degrees C, precisely where it started. What is the mass of the aluminum chunk? 26. When you jog, most of the food energy you burn above your Basal Metabolic Rate (BMR) ends up as internal energy that would raise your body temperature if it were not eliminated. The evaporation of perspiration is the primary mechanism for eliminating this energy. Determine the amount of water you lose to evaporation when running for 30 minutes at a rate that uses 400kcal/h above your BMR. (That amount is often considered to be the “maximum-fat-burning” energy output.) The metabolism of 1g of fat generates approximately 1g of water. (The hydrogen atoms in the fat molecule are transferred to oxygen to form water.) What fraction of your need for water will be provided by fat metabolism? (The latest heat of vaporization of water at room temperature is 2.5 x 10^6 J/kg). 27. A 40g black of ice is cooled to -78 degrees C and is then added to 560g of water in an 80g copper calorimeter at a temperature of 25 degrees C. Determine the final temperature of the system consisting of the ice, water, and calorimeter. (If not all the ice melts, determine how much ice is left.) Remember that the ice must first warm to 0 degrees C, melt, and then continue warming as water. The specific heat of ice is .5 cal/g·˚C = 2090 J/kg·˚C. 51. A 40g ice cube floats in 200g of water in a 100g copper cup; all are at a temperature of 0 degrees C. A piece of lead at 98 degrees C is dropped into the cup, and the final equilibrium temperature is 12 degrees C. What is the mass of the lead?