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Chapter 10: Q.15 (page 256)

How far must you stretch a spring with k = 1000 N/m to store 200 J of energy?

Short Answer

Expert verified

As the all we solve above from that we have , the spring's stretched distance is0.63m.

Step by step solution

01

Introduction

You must exert effort in order to compress or stretch a spring. You must apply a force to the spring that is the same magnitude as the force the spring applies to you, but in the opposite direction. Fext = kx is the force you apply in the direction of the displacement x from its equilibrium position.

02

Explanation

In a compressed or extended spring, the potential energy stored is,

Us=12k(Δs)2

We have, k= spring constant andΔsis the length of the spring compressed or stretched.

Rewriting equation Δs,

Δs=2Usk

Putting 200Jfor Usand 1000N/mfor k, solve for Δs.

Δs=2(200J)1000N/m

=0.63m

As the all we solve above from that we have , the spring's stretched distance is 0.63m.

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Most popular questions from this chapter

A clever engineer designs a “sprong” that obey the force law Fx=-qx-xeq3,where xeq is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity, we’ll let xeq=0m. Then Fx=-qx3.

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 20gplastic ball. What is the launch speed if the sprong constant is 40,000, with the units you found in part a, and the sprong is compressed 10cm? Assume the barrel is frictionless.

In a hydroelectric dam, water falls 25 m and then spins a turbine to generate electricity.

a. What is ∆UG of 1.0 kg of water?

b. Suppose the dam is 80% efficient at converting the water’s potential energy to electrical energy. How many kilograms of water must pass through the turbines each second to generate 50 MW of electricity? This is a typical value for a small hydroelectric dam.

An object moving in the xy-plane is subjected to the force F→=(2xyı^+3yȷ^)N, where x and y are in m.

a. The particle moves from the origin to the point with coordinates (a,b)by moving first along the x-axis to (a,0), then parallel to the y-axis. How much work does the force do?

b. The particle moves from the origin to the point with coordinates (a,b)by moving first along the y-axis to (0,b), then parallel to the x-axis. How much work does the force do?

c. Is this a conservative force?

How much work is done by the environment in the process shown inFIGUREEX10.39? Is energy transferred from the environment to the system or from the system to the environment?

A 10kgbox slides 4.0m down the frictionless ramp shown inFIGURE CP10.72, then collides with a spring whose spring constant is 250N/m.

a. What is the maximum compression of the spring?

b. At what compression of the spring does the box have its maximum speed?
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