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Chapter 9: Q. 18 (page 228)
The two ropes seen in FIGURE are used to lower a kg piano m from a second-story window to the ground. How much work is done by each of the three forces?
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The force acting on a particle is . How much work does this force do as the particle moves along the x-axis from to ?
A horizontal spring with spring constant N/m is attached to a wall. An athlete presses against the free end of the spring, compressing it cm. How hard is the athlete pushing?
Evaluate the dot product if
a. and .
b. and.
A horizontal spring with spring constant N/m extends outward from a wall just above floor level. A kg box sliding across a frictionless floor hits the end of the spring and compresses it cm before the spring expands and shoots the box back out. How fast was the box going when it hit the spring?
Hooke’s law describes an ideal spring. Many real springs are better described by the restoring force , where q is a constant.
Consider a spring with .
It is also.
a. How much work must you do to compress this spring ? Note that, by Newton’s third law, the work you do on the spring is the negative of the work done by the spring.
b. By what percent has the cubic term increased the work over what would be needed to compress an ideal spring? Hint: Let the spring lie along the s-axis with the equilibrium position of the end of the spring at .
Then ∆s = s.
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