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Chapter 7: Q28P (page 172)

During spring semester at MIT, residents of the parallel buildings of the East Campus dorms battle one another with large catapults that are made with surgical hose mounted on a window frame. A balloon filled with dyed water is placed in a pouch attached to the hose, which is then stretched through the width of the room. Assume that the stretching of the hose obeys Hooke’s law with a spring constant of 100 N/m. If the hose is stretched by 5.00 m and then released, how much work does the force from the hose do on the balloon in the pouch by the time the hose reaches its relaxed length?

Short Answer

Expert verified

The work by the hose on the balloon is Ws=1250J

Step by step solution

01

Given data

  1. The spring constant of the hose is,k=100N/m .
  2. The maximum elongation of the hose is,xi=5.00m.
  3. The final position of the hose is, xf=0m.
02

Understanding the concept

We can use the concept of work done by the spring on the block.

Formulae:

Ws=12kxi2-12kxf2

03

Calculate how much work the force from the hose does on the balloon

Work energy theorem states that change in the kinetic energy of the system will be equal to the work done of the system.

The work by the spring is,

Ws=12kxi2-xf2

Substitute the values in the above expression, and we get,

Ws=12×100N/m×5.00m2-0m2Ws=12×100×5.0021N/m×1m2×1J1N·mWs=1250J

Thus, the work by the hose on the balloon is Ws=1250J.

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Most popular questions from this chapter

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’s vertical axis is set byKs=40.0J. If the block’s initial speed is 4.00m/swhat is the normal force on the block?

Figure 7-40 gives the acceleration of a 2.00 kg particle as an applied force Fa→ moves it from rest along an x axis fromx=0tox=9.0m. The scale of the figure’s vertical axis is set byas=6.0m/s2. How much work has the force done on the particle when the particle reaches (a) x=4.0 m, (b) x=7.0 m, and (c) x=9.0 m? What is the particle’s speed and direction of travel when it reaches (d) x=4.0 m, (e) x=7.0 m, and (f) x=9.0 m ?

A spring and block are in the arrangement of Fig. 7-10.When the block is pulled out to x=4.0cm, we must apply a force of magnitude 360N to hold it there.We pull the block to x=11cmand then release it. How much work does the spring do on the block as the block moves from xi=+5.0cmto (a)x=+3.0cm, (b) x=−3.0 cm, (c)x=−5.0 cm ,and (d)x=−9.0 cm ?

In Fig.7-47 , a cord runs around two massless, frictionless pulleys. A canister with mass m 20 kg hangs from one pulley, and you exert a force F→on the free end of the cord. (a) What must be the magnitude ofF→ if you are to lift the canister at a constant speed? (b) To lift the canister by 2.0 cm , how far must you pull the free end of the cord? During that lift, what is the work done on the canister by (c) your force (via the cord) and (d) the gravitational force? (Hint: When a cord loops around a pulley as shown, it pulls on the pulley with a net force that is twice the tension in the cord.)

In Fig. 7-33, a horizontal force F→aof magnitude 20.0Nis applied to a 3.00kgpsychology book as the book slides a distanced=0.500mup a frictionless ramp at angle θ=30.0°. (a) During the displacement, what is the net work done on the book by F→a, the gravitational force on the book, and the normal force on the book? (b) If the book has zero kinetic energy at the start of the displacement, what is its speed at the end of the displacement?
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