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# A spring of force

1. [1 point, 10 tries]A 173 g block is pressed against a spring of force constant 1.68 kN/m until the block compresses the spring 10.1 cm. The spring rests at the bottom of a ramp inclined at 60.7° to the horizontal. Using energy considerations, determine how far up the incline the block moves before it stops if there is no friction between the block and the ramp.Answer:2. [1 point, 10 tries]How far up the incline does the block move before it stops if the coefficient of kinetic friction is 0.470.Answer:3. [1 point, 10 tries]A force acting on a particle moving in the xy plane is given by F = (2.13yi + 1.18×2 j) N, where x and y are in meters. The particle moves from the origin to a final position having coordinates x = 4.26 m and y = 4.26 m, as seen in the figure below.Calculate the work done by F along OAC.Answer:4. [1 point, 10 tries]Calculate the work done by F along OBC.Answer:5. [1 point, 10 tries]A single constant force F = (2.69i + 4.75j) N acts on a 3.54 kg particle. Calculate the work done by this force if the particle moves from the origin to the point having the vector position r = (2.08i – 2.63j) m.Answer:6. [1 point, 10 tries]What is the speed of the particle at r if its speed at the origin is 4.84 m/s?Answer:7. [1 point, 10 tries]What is the change in the potential energy of the system?Answer:8. [1 point, 10 tries]A m = 3.02 kg mass starts from rest and slides a distance d down a frictionless theta = 33.3° incline. While sliding, it comes into contact with an unstressed spring of negligible mass, as shown in the figure below.The mass slides an additional 0.180 m as it is brought momentarily to rest by compression of the spring (k=379 N/m). Calculate the initial separation d between the mass and the spring.Answer:9. [1 point, 10 tries]A potential energy function for a two-dimensional force is of the form U = 2.98×3 y – 6.51x. Calculate the force that acts at the point (1.36 m,1.32 m). Enter the x-component first and then the y-component.Answer 1 of 2:Answer 2 of 2:10. [1 point, 10 tries]An m = 3.09 kg block situated on a rough incline is connected to a spring of negligible mass having a spring constant of k = 101 N/m, as seen in the figure below.The pulley is frictionless. The block is released from rest when the spring is unstretched. The block moves 18.4 cm down the incline before coming to rest. Assume ? = 37.3°. Calculate the coefficient of kinetic friction between block and incline.Answer:11. [1 point, 10 tries]A 4.33 kg block free to move on a horizontal, frictionless surface is attached to one end of a light horizontal spring. The other end of the spring is fixed. The spring is compressed 0.124 m from equilibrium and is then released. The speed of the block is 1.09 m/s when it passes the equilibrium position of the spring. The same experiment is now repeated with the frictionless surface replaced by a surface for which ?k = 0.250. Determine the speed of the block at the (old) equilibrium position of the spring.Answer:12. [1 point, 10 tries]A cylindrical rod 20.9 cm long with a mass of 1.46 kg and a radius of 1.42 cm has a ball with diameter 7.19 cm and mass 2.29 kg attached to one end. The arrangement is originally vertical and stationary, with the ball at the top. The apparatus is free to pivot about the bottom end of the rod. After it falls through 90°, what is its rotational kinetic energy?Answer:13. [1 point, 10 tries]What is the angular speed of the rod and ball after it has fallen through an angle of 90°?Answer:14. [1 point, 10 tries]What is the linear speed of the ball after falling through an angle of 90°?Answer:15. [1 point, 10 tries]What would have been the speed of the ball if it had freely fallen through a distance of 29.6 cm?Answer:16. [1 point, 10 tries]The block m1 with mass 15.0 kg and the block m2 with mass 10.0 kg are suspended by a pulley that has a radius of 10.0 cm and a mass of 3.00 kg, as seen in the figure below.The cord has a negligible mass and causes the pulley to rotate without slipping. The pulley rotates without friction. The masses start from rest d=3.00 m apart. Treating the pulley as a uniform disk, determine the speed of the blocks as they pass each other.Answer:17. [1 point, 10 tries]A 66.1 kg acrobat in training falls from the trapeze and lands in a raised safety net located 13.6 m below him. He stretches the net (which acts as an ideal spring) by 1.45 m. If mechanical energy is conserved while the net is being stretched, what is the elastic potential energy of the net when it is stretched by 1.45 m?Answer:18. [1 point, 10 tries]A 11.3 kg case of bottled water is released from rest down a shipping ramp inclined 32.8° to the horizontal. At the base of the ramp, oriented parallel to its surface, is a spring that can be compressed 1.83 cm by a force of 262 N. The case of water moves down the ramp and compresses the spring by 5.00 cm.How far has the case of water traveled down the ramp from its point of release?Answer:19. [1 point, 10 tries]At what speed is the case moving just as it touches the spring?Answer:20. [1 point, 10 tries]A 1.88 kg rock is dropped onto a spring from a height of 0.415 m. If the spring constant is 1912 N/m, what is the maximum compression of the spring?Answer:Note : please write the answers with their units…thanks

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