4.1.4 The Work Done by a Spring

Question 1

The Work Done by a Spring

Answer 1

• Hooke’s law describes the force of an ideal spring: , where k is the spring constant.
• The force of a spring is in the direction opposite to its displacement, so a spring does negative work when it is stretched or compressed.

Question 2

The force applied by a spring is given by Hooke’s law, F = -kx, where k is the spring constant. The force F is a constant force

Answer 2

false

Question 3

Consider a spring-mass system. The F in Hooke’s law, F = −k x, indicates _____________.

Answer 3

the force on the object by the spring

Question 4

If the work done on an object is negative, how is the object’s speed affected?

Answer 4

The object slows down.

Question 5

Which of the following expresses the work done by a spring on an object that moves from position xi  to xf ?

Answer 5

W = integral from xi to xf of (-kx)dx

Question 6

If we decrease the displacement of an object attached to a spring, the magnitude of the force on the object __________________.

Answer 6

decreases

Question 7

If an object attached to a spring is released after being stretched, the object moves to the left and passes the equilibrium point. What is the direction of the force applied by the spring when the object is to the left of the equilibrium point?

Answer 7

To the right

Question 8

What is the general formula for the work done by a spring in moving an object from an initial position xi  to a final position xf ?

Answer 8

• W = k(xi^2/2 - xf^2/2)

- W = -k(xf^2/2 - xi^2/2)

Question 9

What does the minus sign in Hooke’s law,

F = −k x, indicate?

Answer 9

The direction of the force is opposite to the displacement.

Question 10

Tow springs have spring constant k1 and k2, where k2>k1. Which spring is stiffer?

Answer 10

Spring 2