Hooke's Law and Elastic Potential Energy

Hooke's Law and

Elastice Potential Energy

Chapter 7 - Etkina

The force exerted on a spring results in a stretch (or compression) of the spring.

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Hooke's Law

Multiple Choice

The graph shows the stretching of two different springs, A and B, when different forces were applied. Which spring is stiffer?

• A

• B

• They have the same stiffness

Multiple Choice

What feature of the F vs. x graph informs you on the spring stiffness?

• The area under the curve.

• The slope.

• The sum of the interval constants.

Multiple Choice

Determine the spring constant for Spring A.

• 32 N/m

• 32 m/N

• 80 N/m

• 80 m/N

Multiple Choice

Determine the spring constant for Spring B.

• 50 N/m

• 50 m/N

• 20 N/m

• 20 m/N

Multiple Choice

A spring is attached to the floor and is pulled straight up by a string. The string's tension is measured. The graph shows the tension in the string as a function of the spring's length. Does this obey Hooke's Law.

• Yes, because the graph has a positive slope.

• Yes, because the spring length increases linearly with applied force.

• No, because the graph would have a negative y intercept.

• No, because the T vs. L relationship is invalid.

Multiple Choice

What is the spring constant for this spring?

• 0.5 N/m

• 50 N/m

• 10 N/m

• 100 N/m

Restoring Force

In physics, some textbooks refer to the F_{spring on object} as the

restoring force

since the spring is "trying" to pull itself back into equilibrium (it's unstretched position).

You need to know this for the next question...

Fill in the Blanks

A spring has an unstretched length of 10 cm. It exerts a restoring force F when stretched to a length of 11 cm. For what length, in cm, of the spring is its restoring for 3F? Enter a numeric value only.

Remember, k is a constant for a given spring, so the ratio of force to spring stretch must be constant.

Multiple Choice

The left end of a spring is attached to a wall. When Babs pulls on the right end with a 200 N force, she stretches the spring by 20 cm. The same spring is then used for a tub-of-war between Babs and Casey. Each pulls on their end of the spring with a 200 N force. How far does Bab's end of the spring move?

• 10 cm

• 20 cm

Multiple Choice

A mass hung from a spring stretches the spring by 4.0 cm. If the same mass is hung from a second spring having half the spring constant as the first, by how much will the second spring stretch?

• 8.0 cm, because with half the spring constant, the spring will stretch twice as far due to the linear relationship.

• 2.0 cm, because with half the spring constant, the spring will stretch half as far due to the directly proportional relationship.

• Not enough information is given to answer this question.

If you got that last one wrong

The force is constant for both springs...

F = (4cm) k F = (Δx)(1/2 k)

so (4cm) k = (Δx)(1/2 k)

k cancels, thus 4 = (1/2)Δx

So the new stretch is 4 x 2 = 8 cm

​Elastic Potential Energy

Multiple Choice

You pull on a spring which obeys Hooke's Law, in two steps. In step 1 you extend it by distance x_s. In step 2, you further extend it by the same distance, x_s. Choose the answer that correctly compares the elastic potential energy of the spring after the first step (U_s1) with that after the second step (U_s2).

• U_s2 = 2U_s1

• U_s2 < 2U_s1

• U_s2 > 2U_s1