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Test III Summary Test III Summary Level : Physics I Instructor : Kim You are in car traveling 50mph and if the car suddenly stopped, would you fly forward or backward? Use Newton’s 1st law to explain to justify your answer. Please be thorough in your explanation. A passenger in a bus notices that a ball which has been at rest in the aisle suddenly starts to roll toward the front of the bus. What can the passenger conclude about the motion of the bus from this observation? Use Newton’s 1st law to explain. Please be thorough in your explanation. To dislodge ketchup from the bottom of a ketchup bottle, it is often turned upside down and thrust downward at high speeds and then abruptly halted. Explain how this works using Newton’s 1st law. Please be thorough in your explanation. I. Without Friction 1. A crate with a mass of 23kg accelerates along a frictionless surface as the crate is pulled with a force of 14.5N at an angle of θ=19°, as shown below. What is the horizontal acceleration of the crate? Fapp θ ans) 0.60m/s2 2. Two forces act on a 4.5kg block resting on a frictionless surface as shown below. What is the horizontal acceleration of the block? F1 =5.9N, F2=3.7N and θ=43° F1 F2 θ Ans) 0.14m/s2, right 3. How much force is needed to give a 5kg block an acceleration of 2m/s² up the 30º incline plane? Assume the inclined plane is frictionless. Fapp Ans) 34.5N 4. An 8kg box is released on a 30º inclined plane and slides down a frictionless inclined plane. i) Find the acceleration of the box. ii) Does the mass affect the motion of the box? Ans) 4.9m/s2 5. A box of mass 1.7kg is sliding on a frictionless flat surface with a speed of 4.2m/s. The angle of the ramp is θ =13° and the surface of the ramp is also frictionless. i) What is the acceleration of the box when it is sliding up the ramp? ans) 2.2m/s2 down the incline ii) How far will the box slide up the ramp? ans) 4m iii) When the box is sliding down, what is the acceleration? ans) 2.2m/s2 down the incline 6. A 1.4kg block pushed along a frictionless 22° inclined plane. A force of Fapp=6N acting parallel to the incline and up the incline is applied to the block. You want the block to move up the ramp at a constant speed. How much force Fapp do you need to apply now? Fapp ans) 5.14N II. With Friction ∑F=ma, f = μ FN 7. Suppose that a 12kg box is pulled by a 45N force parallel to a rough surface. The coefficient of kinetic friction μk is 0.2. Find the acceleration of the box. Fapp Ans) 1.8m/s2 8. A 60kg crate rests on the level floor at a shipping dock. The coefficient of static friction and coefficient of kinetic friction is μs= 0.760 and μk = 0.410, respectively. What horizontal force is required to i) just start the crate moving and ii) slide the crate across the dock at constant speed? ans) 447N, 241N 9. A crate of mass 100kg with an initial speed of 7.6m/s is gliding across the ice. The coefficient of kinetic friction is μk = 0.1. Find the acceleration and how far the crate will travel before coming to a rest. (*~the only force acting horizontally is the frictional force acting in the opposite direction of 2 2 the motion. Use vf -vi =2ax to find the distance) ans) -0.98m/s2 , 29.5m 10. i) How much force is needed to move a 10kg block at constant speed up along 40º inclined plane if μk is 0.3? Fapp ans) 85.5N 2 ii) How much force is needed to give a 10kg block an acceleration of 3m/s up the 40º incline if μk is 0.3? ans) 115.5N 11. An 8kg box is released on a 30º inclined plane and accelerates down the plane. The coefficient of kinetic friction μk = 0.54. Find the acceleration of the box. (*~the box is sliding due to gravity, so there is no applied force) ans) 0.32m/s2 ∑F=ma, f = μ FN 12. i) A 8kg box is released from rest on a 30° inclined frictionless plane and accelerates down the incline. If the distance from the block to the end of the ramp is 4m, what is the speed of the block when 2 2 it reaches the bottom of the ramp? (use vf -vi =2ax to find ‘v’) ans) 6.3m/s ii) Let’s say the surface of the inclined plane is rough. The coefficient of kinetic friction is μk = 0.25. What is the speed of the block when it reaches the bottom of ramp? ans) 4.7m/s 13. A box is given an initial push. The box is sliding up an incline that makes an angle of 15° with respect to the horizontal. The coefficient of kinetic friction between the box and the surface of the incline is μk =0.18. The initial speed of the box at the bottom of the incline is 1.5m/s. How far does the box travel along the 2 2 incline before coming to rest? (hint: use vf -vi =2ax to find ‘x’) ans) 0.265m 14. 8kg box is released from rest on a 30° inclined rough plane and accelerates down the incline. The coefficient of friction of the incline plane is µk=0.54. i) If the distance from the block to the end of the ramp is 4m, what is the speed of the block when it reaches 2 2 the bottom of the ramp? (use vf -vi =2ax to find ‘v’) ans) 1.6m/s ii) The block will eventually slide off the ramp and continue on the surface. If the coefficient of kinetic 2 2 friction on the surface was µk=0.12, how far will the block travel until it stops? (use vf -vi =2ax to find ‘x’) ans) 1.09m ∑F=ma, f = μ FN 15. Suppose that a 70kg box is pulled by a 400N force at an angle of 30° to the horizontal. The coefficient of kinetic friction μk is 0.5. Find the acceleration of the box. Fapp 30° a) 1.48m/s2 16. A block of mass 10kg is resting on flat surface. The coefficient of static friction μs=0.5. If the block is pulled at an angle of 30° what is the minimum force needed to move the object? Fapp 30° ans) 43.9N 17. An object of mass 5kg on a flat surface is pulled at an angle of 30°, where the coefficient of kinetic friction μk= 0.113. How much force is needed to move the object at a constant speed? Fapp 30° ans) 6N 18. A girl is pulling a sled with a mass of 16kg across a level patch of grass by exerting a force of 50N along a rope that forms an angle of 33° above the ground. i) If the coefficient of kinetic friction between the sled and the grass is μk = 0.25, find the acceleration of the sled.\ Fapp 33° ans) 0.6m/s2 ii) The girl gets tired and reduces her pulling force to 22N on the sled. Find the acceleration of the sled. ans) -1.1m/s2 ∑F=ma, f = μ FN 19. A m1=6kg block is on a horizontal surface. The coefficient of kinetic friction is µk=0.22. The mass of the hanging block is m2=3kg. Find the acceleration a of both blocks and the tension T. m1 m2 ans) a=1.83m/s2, T=23.9N 20. The coefficient of kinetic friction between block m1 and the table is µk=0.2. Also, m1=25kg, m2=15kg. A horizontal force of Fapp=250N is pulling on the m1. What is the acceleration of the system? The system is moving to the left m1 Fapp m2 ans) 1.35m/s2 21. The coefficient of kinetic friction between block m1 and the table is µk=0.24. Also, m1=3.5kg, m2=2.2kg. m1 Fapp m2 i) Find the horizontal force needed to move the blocks at a constant speed. ans) 30N ii) Find the horizontal force needed to move the blocks to have an acceleration of 2.4m/s2 ans) 44N .
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