force and energy

Question

An ideal spring obeys Hooke’s law: F~ = −k ~x. A mass of m = 0.6 kg hung vertically from this spring stretches the spring 0.1 m. The acceleration of gravity is 9.8 m/s 2 . Calculate the value of the force constant k for the spring.

Answer in units of N/m.

Answer 1

Hi Grace,

Let's look at the free body diagram of the hanging mass first. In the downward direction, we have the force due to gravity, or the weight, of the mass. In the upward direction, we have the spring force. Therefore, the spring force has the same magnitude of the gravity force, which in this case is mg, or 0.6*9.81, or 5.886N.

Now, in order for the spring to provide this force, it must displace some distant x given by Hooke's law. That negative sign will get canceled out by our displacement (since the displacement is in the negative y direction). So our spring force must be 5.886N, which is equal to spring constant times the magnitude of the displacement, 5.886 = k*(0.1). If we divide 0.1 by both sides, we get that the spring constant is equal to 58.86N/m.

Hope this helps!