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Chapter 9: Q.50 (page 229)

You鈥檙e fishing from a tall pier and have just caught a 1.5kgfish. As it breaks the surface, essentially at rest, the tension in the vertical fishing line is 16N. Use work and energy to find the fish鈥檚 upward speed after you鈥檝e lifted it 2.0m.

Short Answer

Expert verified

The speed of the fish when it is lifted2mabove the water surface is1.9m/s

Step by step solution

01

Content Introduction

The work done by constant force is

W=Fnet.鈭�r=Fnet.鈭�r(cos胃)

Considering the following free body diagram,

The net force is calculated as

Fnet=T-FGFnet=T-mg

The work done by net force is

localid="1647791833780" W=Fnet.鈭�r(cos胃)W=(T-mg).鈭�r(cos胃)W=(16N-1.5kg脳9.81m/s2)(2.0m)(cos0掳)W=2.6J

02

Content Explanation

According to work energy theorem, work done by the net force is equal to the change in kinetic energy. Therefore,

鈭�K=W12m(vf2-vi2)=Wvf=2Wm+vi2

Substitute the values and evaluate

vf=2(2.6J)1.5kg+(0m/s)2vf=1.9m/s

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Most popular questions from this chapter

Two identical horizontal springs are attached to opposite sides of a box that sits on a frictionless table. The outer ends of the springs are clamped while the springs are at their equilibrium lengths. Then a 2.0N force applied to the box, parallel to the springs, compresses one spring by 3.0cm while stretching the other by the same amount. What is the spring constant of the springs?

A 12kgweather rocket generates a thrust of 200N.The rocket, pointing upward, is clamped to the top of a vertical spring. The bottom of the spring, whose spring constant is 550N/m, is anchored to the ground.

a. Initially, before the engine is ignited, the rocket sits at rest on top of the spring. How much is the spring compressed?

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A 25kg air compressor is dragged up a rough incline from r1鈫�=(1.3i^+1.3j^)m to r2鈫�=(8.3i^+2.9j^)m, where they-axis is vertical. How much work does gravity do on the compressor during this displacement?

A 5.0kg mass hanging from a spring scale is slowly lowered onto a vertical spring, as shown in the FIGURE. The scale reads in newtons.

a. What does the spring scale read just before the mass touches the lower spring?

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The gravitational attraction between two objects with masses m1 and m2, separated by distance x, is F=Gm1m2/x2 , where G is the gravitational constant.

a. How much work is done by gravity when the separation changes from x1 to x2? Assume x2<x1.

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