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A clever engineer designs a “sprong” that obeys the force
Chapter 11, Problem 60P(choose chapter or problem)
Problem 60P
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, we’ll let xe = 0 m. Then Fx = − qx3.
a. What are the units of q ?
b. Find an expression for the potential energy of a stretched or compressed sprong.
c. A sprong-loaded toy gun shoots a 20 g plastic ball. What is the launch speed if the sprong constant is 40,000, with the units you found in part a, and the sprong is compressed 10 cm? Assume the barrel is frictionless.
Questions & Answers
QUESTION:
Problem 60P
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, we’ll let xe = 0 m. Then Fx = − qx3.
a. What are the units of q ?
b. Find an expression for the potential energy of a stretched or compressed sprong.
c. A sprong-loaded toy gun shoots a 20 g plastic ball. What is the launch speed if the sprong constant is 40,000, with the units you found in part a, and the sprong is compressed 10 cm? Assume the barrel is frictionless.
ANSWER:
Step 1 of 3
a) We need to find out the unit of \(q\).
The unit of \(q\) is \(N / m^{2}\).