± Hooke\'s Law Learning Goal: To understand the use of Hooke\'s law for a spring

Question

± Hooke's Law

Learning Goal:

To understand the use of Hooke's law for a spring.

Hooke's law states that the restoring force F  on a spring when it has been stretched or compressed is proportional to the displacement x  of the spring from its equilibrium position. The equilibrium position is the position at which the spring is neither stretched nor compressed.

Recall that F x  means that F  is equal to a constant times x . For a spring, the proportionality constant is called the spring constant and denoted by k. The spring constant is a property of the spring and must be measured experimentally. The larger the value of k, the stiffer the spring.

In equation form, Hooke's law can be written

F =kx .

The minus sign indicates that the force is in the opposite direction to that of the spring's displacement from its equilibrium length and is "trying" to restore the spring to its equilibrium position. The magnitude of the force is given by F=kx, where x is the magnitude of the displacement.

Part B

After driving a portion of the route, the taptap is fully loaded with a total of 24 people including the driver, with an average mass of 62 kg per person. In addition, there are three 15-kg goats, five 3-kg chickens, and a total of 25 kg of bananas on their way to the market. Assume that the springs have somehow not yet compressed to their maximum amount. How much are the springs compressed?

Enter the compression numerically in meters using two significant figures.

............

............

Explanation / Answer

First, solve for the total mass loaded onto the taptap:

m = (24 * 65) + (3 * 15) + (5 * 3) + 25
m = 1645 kg

And the gravitational force (the weight of everything loaded in the taptap) is:

F = mg
F = 1645 *9.8
F = -16121 N (negative because the force is downward)

Using the k , solve for x:

F = -kx

x = F/-k = -16121/-k

The value of k is not given in the problem. So Put k in above formula and find x in meters.

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