Example Problems 5.1 Force and Acceleration E1. A monkey pushes his pet lemur in a wagon with a net force of 38 N. If the mass of the lemur and wagon combined is 57 kg, calculate the acceleration of the wagon. E2. To catch a 0.5 kg softball, a monkey applies a net force of 25 N. Calculate the magnitude and the direction of the acceleration of softball. 1
E3. A tennis ball, 0.314 kg, accelerates off a racket at rate of 164 m/s² when hit by a professional tennis player. Calculate the force the player s racket exert on the ball. E4. A car of mass 2300 kg slows down at a rate of 3.0 m/s² when approaching a stop sign. What is the magnitude of the net force acting on the car as it slows down? 2
E5. A crate filled with cocoanuts is pushed across an ice-covered lake by a monkey. The monkey pushes on the crate with a force of 47 N causing the crate to accelerate at 0.08 m/s², calculate the total mass of the crate. b) E6. A dragster, starting from rest and attains a speed of 58.9 mph (26.3 m/s) in 0.59 seconds. If the dragster has a mass of 873 kg, calculate the average acceleration of the and the magnitude of the net force acting on the dragster. v o = v f = t = b) 3
E7. A student pushes a loaded sled whose mass is 240 kg for a distance of 2.3 meters over the frictionless surface on a frozen lake. The student exerts a constant horizontal force of a magnitude 130 N. If the sled starts from rest, what is its final velocity? v o = v f = d = t = b) E8. The student in previous problem wants to reverse the direction of the velocity of the sled in 4.5 seconds. With what constant force must he push on the sled to do so? v o = v f = t = b) 4
Student Problems 5.1 Force and Acceleration 1. With each step a runner takes, he exert a force of 59 N on the ground. If the runner s mass is 58 kg, calculate the acceleration the runner undergoes. 2. A monkey pushes a crate full of coconuts with a force of 85.5 N. If the total mass of the crate is 24.3 kg, calculate the acceleration of the cart. 5
3. A crazy monkey takes a suitcase and throws it across the room. If the suitcase has a mass of 25 kg and is accelerated from rest at 2.2 m/s², how much force did the monkey exerted on the suitcase as he threw it across the room? b) 4. A tow-cable can withstand a maximum tension of 1,000 N. A monkey offer to help a friend tow his broken down car to a repair shop. If the car has a mass of 2,100 kg, what is the maximum acceleration the car can be pulled before the cable breaks? b) 6
5. A 4 kg objects rests on a frictionless horizontal surface. Calculate the magnitude of the horizontal force that is required to give the object an acceleration of 3 m/s². 6. A monkey pulls his pet lemur in a wagon with a net force of 110 N. The wagon accelerates at 2.5 m/s², calculate the total mass of the wagon with the lemur. 7
7. A sports car accelerates from 0 to 60 mph, (0 m/s - 27 m/s), in 4.3 seconds. The car exerts a force of 4106 N, calculate the mass of the car. v o = v f = t = b) 8. A monkey-mobile, mass 1,430 Kg, is heading north at 26.82 m/s when the brakes are applied causing the vehicle to slow and come to rest in 2.32 seconds. If the average force acting on the vehicle is 16,530.8 N, calculate the acceleration and the direction of the acceleration as the vehicle is brought to rest. v o = v f = t = b) 8
9. A 204.11 kg motorcycle accelerates from rest to 24.59 m/s in 6.0 seconds. What is the magnitude of the average acceleration and the net force acting on the motorcycle? v o = v f = t = b) 10. A crazy monkey is driving his car at 10 m/s when he hits a tree causing the car to come to rest in 0.10 seconds. If the combined mass of the car and the monkey is 1,200 kg calculate the acceleration of the car and net force that brings the car to rest. v o = v f = t = b) 9
11. A 0.149 kilogram baseball, initially moving at 100 mph (45 m/s), is brought to rest in 0.040 second as it is caught in the glove of a catcher. Calculate the acceleration and the net force exerted on the ball as it is caught in the glove. v o = v f = t = b) 12. In the diagram, a 12 N force is being applied to two blocks, A and B, initially at rest on a horizontal, frictionless surface. Block A has a mass of 1.0 kilogram and block B has a mass of 2.0 kilograms. Find the magnitude of the acceleration of block B and the force acting on block B. b) 10
Monkey Busters 5.1 Force and Acceleration 13. A block, initially at rest on a friction-free horizontal plane, is acted on by a horizontal force of 25 N. In 4 seconds the block travels 40 meters, what is the blocks mass? b) 14. A crate whose mass is 360 kg rests on the bed of a truck that is moving at a speed of 120 km/h. The driver applies the brakes and slows to a speed of 62 km/h in 17 seconds. What force (assumed constant) acts on the crate during this time? Assume that the crate does not slide on the truck bed. b) 11
15. What is the average force exerted by a shot-puter on a 7.0 kg shot if the shot is moved through a distance of 2.8 meters and is released with a speed of 13 m/s? b) 16. A person has a reasonable chance of surviving an automobile crash if the deceleration is no more than 30 g s. Calculate the force on a 70 kg person accelerating at this rate. What distance is traveled if brought to rest at this rate from 55 mph (24.59 m/s)? b) 12
Monkey Busters 5.1 Force and Acceleration (Angles) 17. A block of mass 2 kg sits idle on a frictionless horizontal surface. The block is pulled by a 10 N force from a rope that makes an angle of 37 with horizontal. Calculate the acceleration of the block the magnitude of the normal reaction force of the supporting surface on the block. b) 18. On April 4, 1974, John Massis moved two railroad passenger cars with his teeth. Massis pulled (with his teeth) on his end of the rope with a constant force that was 2.5 times his body weight, at an angle of 30 from the horizontal. His mass was 80 kg. The weight of the passenger cars were 7.0 X 10 5 N (about 80 tons), and he moved them 1.0 m along the rails. Assume the wheels encountered no retarding force from the rails as they rolled. What was the speed of the train just at the end of the pull? 13
19. A mass is pulled across the floor by a force of 100 N by a string. The string makes an angle of 60 with the horizontal. If the acceleration of the block is 1.5 m/s², what is the mass of the block? b) 20. A car rolls from rest down a 200 meters long hill. The elevation difference between the top of the hill and the bottom is 25 meters. If frictional forces are negligible, what is the speed of the car when it reaches the bottom of the hill? b) 14
21. A block of mass 15 kg is held by a cord on a frictionless inclined plane. If the angle of the inclined plane is 27, calculate the tension in the cord and the force the plane exert on the block. Suppose you cut the cord holding the block, calculate the acceleration of the block down the plane. 22. A 2.00 kg mass slides down a frictionless inclined plane that makes an angle of 30 with horizontal. The mass starts from rest. What is its speed after it has slipped a distance of 3.00 meters? b) 15
23. A block of initially at rest, slides down an inclined plane that makes an angle of 30 with the horizontal. After it has slid a distance of 8 m, its speed is 5 m/s, calculate the mass of the block. b) 24. The smooth wooden triangular block of mass M slides on a friction-free horizontal table. ( Describe the motion of the block if the block and the mass m on its inclined surface are left free to move under the influence of gravity. (There is also no friction between the mass and the inclined surface of the block.) (b) How large a horizontal force F must be applied to the triangular block to prevent its motion? (c) What should the acceleration of the block be to maintain the mass at constant height? (d) How large a force is needed to provide the acceleration in (c)? 16