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

Question

Learning Goal: To understand the use of Hooke's law for a spring.
Hooke's law states that the restoring force on a spring when it has been stretched or compressed is proportional to the displacement of the spring from its equilibrium position. The equilibrium position is the position at which the spring is neither stretched nor compressed. Recall that means that is equal to a constant times . For a spring, the proportionality constant is called the spring constant and denoted by . The spring constant is a property of the spring and must be measured experimentally. The larger the value of , the stiffer the spring.In equation form, Hooke's law can be written.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 , where is the magnitude of the displacement.

A)A 60KG- driver gets into an empty taptap to start the day's work. The springs compress 0.02m . What is the effective spring constant of the spring system in the taptap?Enter the spring constant numerically in newtons per meter. Express your answer using two significant figures.

Explanation / Answer

Hooke's Law states that: F = -k*x, where x is the displacement of the spring. In the example, we know that the gravitational force exerted on the driver balances with the restoring force provided by the spring. So, mg = k*x (dealing with magnitudes only, since we know that the directions are different. Then, k = m * g / x So k = 9.8 * 60 /0.02 = 29 400 N/m. So, to two significant figures, k = 29 000 N/m.

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