During spring semester at MIT, residents of the parallel buildings of the East C

Question

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 and has a spring constant of 93 N/m. If the hose is stretched by 5.2 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?

Explanation / Answer

k =93 N/m ,x =5.2 m

Spring force is conservative force

Work done by conservative force is expresses as change in potetIal energy

W =Ui -Uf

W =(1/2)kx^2 -0

W = 0.5*93*5.2*5.2

W =1257.36 J

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