10.8.3 Hooke's Law

Question 1

Hooke’s Law

Answer 1

• Work is the energy used when applying a force over a distance.
• Use Hooke’s law to determine how much force it takes to stretch a spring.

Question 2

note

Answer 2

• When you stretch out a spring, it gets harder to stretch as the length of the spring increases.
• You can use Hooke’s law to determine how much force it takes to stretch a spring.
• Springs all have a resting length. The resting length is how long the spring is before you stretch it.
• The variable x represents the spring’s extension from its resting length. If the spring is 3 inches long at rest and you stretch it to 5 inches, then you have extended it 2 inches.
• The constant k is called the spring constant. Each spring has its own spring constant. Often you will have to determine this value from information you are given.
• Here is an example of Hooke’s law in action.
• Suppose you are given a spring whose resting length is two inches and you know that it takes five pounds to stretch the spring to ten inches.
• To calculate the work done by stretching the spring you first have to determine the spring constant.
• You know that to extend the spring ten inches requires a five-pound force. Plug those values into Hooke’s Law to find the spring constant.
• Once you have the spring constant you can integrate the force equation to determine the work required to stretch the spring to any length.
• Here the spring is stretched twelve inches, so integrate from zero to twelve.

Question 3

The unstretched length of a certain spring is known to be 5 in. When a 60 lb weight is placed on top of this spring, the spring compresses to a length of only 3 in. Determine the spring constant.

Answer 3

30 lb/in

Question 4

A 150 lb person sits on a spring-mounted chair whose spring has a stiffness of 200 lb/in. How far does the chair sink when the person sits down?

Answer 4

0.75 in.

Question 5

It takes 10 lb of force to stretch a spring 2 in. What is the stiffness (spring constant) of the spring?

Answer 5

5 lb/in

Question 6

How much work is done stretching a spring with a stiffness of 25 lb/in a distance of 5 in?

Answer 6

312.5 lb-in

Question 7

How much work is done stretching a spring with a stiffness of 20 lb/in a distance of 5 in?

Answer 7

250 lb-in

Question 8

How much work is done by stretching a spring with a stiffness of 10 N/m a distance of 10 cm?

Answer 8

0.05 N-m

Question 9

Which of the following is not an acceptable value for a spring constant k (in units of lb/in)?

Answer 9

−1

Question 10

Hooke’s law applies to ideal springs, whose force is proportional to the distance it is compressed or stretched. Some springs, however, are designed to differently. Consider a spring whose force can be described by F (x) = 2x + 3x ^2, where the force is expressed in newtons and x is expressed in centimeters. How much work is done by stretching this spring 5 cm?

Answer 10

150 N-cm

Question 11

For a science fair, a group of students are designing a spring-powered “cannon” to shoot a tennis ball a certain distance across the classroom (at another group’s “castle”). The idea is to compress a spring a certain amount, place a tennis ball on top of the spring, and then place a tube over both to aim the ball. When a lever is depressed the spring will be released, and all of the work done by the spring will be converted into the kinetic energy of the tennis ball, firing it across the room. Based on other calculations, the students have determined that they want the tennis ball to leave the tube with a kinetic energy of 40 lb-in. They’ve measured their spring constant at 5 lb/in. How much should the spring be compressed to achieve this kinetic energy when the “cannon” is fired?

Answer 11

4 in

Question 12

Which of the following requires the greatest work?

Answer 12

Stretching a spring with a constant of 3 lb/in a distance of 5 inches.