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Chapter 7: 36P (page 173)

A 5.0 kg block moves in a straight line on a horizontal frictionless surface under the influence of a force that varies with position as shown in Fig.7-39. The scale of the figure鈥檚 vertical axis is set byFs=10.0N. How much work is done by the force as the block moves from the origin to x=8.0cm?

Short Answer

Expert verified

The net work done by the force using a graph W=25J.

Step by step solution

01

Given

  1. The mass of block is, m=5.0kg
  2. The scale for vertical axis is, Fs=10.0N
02

Understanding the concept

We can use the concept that the work done is equal to the area under the curve for a graph.

Formula:

W=鈭�xixfF(x)dxA=12脳base脳heightA=length脳breadth

03

Calculate the net work done

We know that the total area will be the net work done by the force.

So,

W=W1+W2+W3+W4

Substitute all the value in the above equation.

W=10N脳2m+12脳10N脳2m+0+-12脳2N脳5mW=25J

Therefore, the net work done is 25J

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Most popular questions from this chapter

A can of bolts and nuts is pushed 2.00 m along an x axis by a broom along the greasy (frictionless) floor of a car repair shop in a version of shuffleboard. Figure 7-26 gives the work Wdone on the can by the constant horizontal force from the broom, versus the can鈥檚 position x. The scale of the figure鈥檚 vertical axis is set by WS=6 J. (a) What is the magnitude of that force? (b) If the can had an initial kinetic energy of 3.00 J, moving in the positive direction of the x axis, what is its kinetic energy at the end of the 2.00 m?

A block is sent up a frictionless ramp along which an x axis extends upward. Figure 7-31gives the kinetic energy of the block as a function of position x; the scale of the figure鈥檚 vertical axis is set byKs=40.0J. If the block鈥檚 initial speed is 4.00m/swhat is the normal force on the block?

Figure 7-27 shows an overhead view of three horizontal forces acting on a cargo canister that was initially stationary but now moves across a frictionless floor. The force magnitudes are F1=3.00N, F2=4.00N, and F3=10.00N, and the indicated angles are 胃2=50.0掳and 胃3=35.0掳. What is the net work done on the canister by the three forces during the first 4.00 m of displacement?

As a particle moves along an x axis, a force in the positive direction of the axis acts on it. Figure 7-50shows the magnitude Fof the force versus position x of the particle. The curve is given by F=a/x2, with a=9.0N.m2. Find the work done on the particle by the force as the particle moves fromx=1.0mto x=3.0mby (a) estimating the work from the graph and (b) integrating the force function.

In Fig.7-30, a block of ice slides down a frictionless ramp at angle 胃=50鈭�while an ice worker pulls on the block (via a rope) with a force F鈫�that has a magnitude of 50Nand is directed up the ramp. As the block slides through distance d=0.50malong the ramp, its kinetic energy increases by . How much greater would its kinetic energy have been if the rope had not been attached to the block?
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