30.03.2023 - 13:26

A clever engineer designs a “sprong” that obeys the force law Fx = -q(x – xe )^3, where xe is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity well let xe = 0 Then Fx = -qx^3. a) What are the units of q? b) D

Question:

A clever engineer designs a ‘sprong’ that obeys the force law Fx = -q(x – xe ){eq}^3 {/eq}, where xe is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity well let xe = 0 Then Fx = -qx{eq}^3 {/eq}.

a) What are the units of q?

b) Draw a graph of Fx vs. x.

c) Find an expression for the potential energy of a stretched or compressed spring.

d) A sprong-loaded toy gun shoots a 20 g plastic ball. What is the launch speed if the spring constant is 40,000, with the units you found in part a, and the spring is compressed 10 cm? Assume the barrel is frictonless.

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