Question Rubber bands and springs do not apply a constant force. Instead the for

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Rubber bands and springs do not apply a constant force. Instead the force they apply is proportional to the amount by which they're stretched or compressed. You have a slingshot. You use the force probe and motion sensor to measure how much force it takes to stretch the slingshot's elastic by different amounts. Your results are shown in the graph.

a. What is the work done to pull the slingshot back 80.0 cm? Describe how you find the work using the data given.

b. A mean kid takes your slingshot and loads it with a 50.0 g rock. The kid holds the loaded slingshot 1.0 meter off the ground. Before the rock is released what kind(s) of energy does it have?

c. The rock is released. How fast will it be going as soon as it's free of the rubber band?

d. The rock is launched horizontally at a height of 1.0 m above the ground. The moment before it hits the ground, what kind(s) of energy does the rock have? What will be its overall speed when it hits the ground?

Explanation / Answer

a) from the graph it can be seen that the force is 30N at 0.8m stretch.

F=kx

=> k = 37.5 N/m

K - spring constant.

since work dW = F.dx

=> dW = (kx)*dx

integrating this we get

W = (1/2) k*x^2

W = 0.5*37.5*0.8*0.8

W = 12J.

This work can also be found from the graph.

Work is equal to the area under the Force vs Displacement graph.

So calculating the area under the graph, we get the work done.

B) The rock has two kinds of energy.

1) gravitational potential energy = m*g*h = 0.05*9.8*1 = 0.49 J

2) spring potential energy = 1/2*k*x*x = 12J

C) all the spring potential energy is converted into the kinetic energy of the rock

=> 1/2*k*x*x = 1/2*m*v*v

=> 37.7*0.8*0.8 = 0.05*v*v

=> v = 21.908 m/s.

D) As it hits the ground it has kinetic energy only.

its horizontal speed remains the same. its acquires vertical downward speed

Vv = sqrt(2*g*h)

Vv = 4.42 m/s..

so it has horizontal speed of 21.908 m/s

and vertical speed of 4.42 m/s

The overall speed becomes zero when it hits the ground.

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