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Chapter 10: Q.41 (page 258)
A very slippery ice cube slides in a vertical plane around the inside of a smooth, -diameter horizontal pipe. The ice cube鈥檚 speed at the bottom of the circle is . What is the ice cube鈥檚 speed at the top?
Ice cube's speed at the top will be zero.
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a. With what minimum speed must you toss a ball straight up to just touch the -high roof of the gymnasium if you release the ball above the ground? Solve this problem using energy.
b. With what speed does the ball hit the ground?
The maximum energy a bone can absorb without breaking is surprisingly small. Experimental data show that the leg bones of a healthy, 60 kg human can absorb about 200 J. From what maximum height could a 60 kg person jump and land rigidly upright on both feet without breaking his legs? Assume that all energy is absorbed by the leg bones in a rigid landing
A clever engineer designs a 鈥渟prong鈥� that obey the force law ,where is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity, we鈥檒l let . Then .
a. What are the units of q?
b. Find an expression for the potential energy of a stretched or compressed sprong.
c. A sprong-loaded toy gun shoots a plastic ball. What is the launch speed if the sprong constant is , with the units you found in part a, and the sprong is compressed ? Assume the barrel is frictionless.
A sled starts from rest at the top of the frictionless, hemispherical, snow-covered hill shown in FIGURE CP10.74.
a. Find an expression for the sled鈥檚 speed when it is at angle .
b. Use Newton鈥檚 laws to find the maximum speed the sled can have at angle without leaving the surface.
c. At what angle does the sled 鈥渇ly off鈥� the hill?
A particle with the potential energy shown in FIGURE Q10.8 is moving to the right at x = 5 m with total energy E.
a. At what value or values of x is this particle鈥檚 speed a maximum?
b. Does this particle have a turning point or points in the range of x covered by the graph? If so, where?
c. If E is changed appropriately, could the particle remain at rest at any point or points in the range of x covered by the graph? If so, where?
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