Question

A spring has a length of (0.200 m) when a (0.300 kg) mass hangs from it, and a length of (0.750 m) when a (1.95 kg) mass hangs from it.

a) What is the force constant of the spring?
b) What is the unloaded length of the spring?

a) (12.0 N/m), (0.120 m)
b) (15.0 N/m), (0.150 m)
c) (18.0 N/m), (0.180 m)
d) (20.0 N/m), (0.200 m)

Answer 1

To find the force constant of the spring, use Hooke's Law. Rearrange the equation to solve for the force constant. To find the unloaded length of the spring, use the equation x = mg/k.

Step-by-step explanation:

To find the force constant of the spring, we can use Hooke's Law which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. We can use the equation F = kx, where F is the force, k is the force constant, and x is the displacement.

For the first case, with a 0.300 kg mass and a spring length of 0.200 m, we can rearrange the equation to solve for the force constant k. Plugging in the values, we have F = (0.300 kg)(9.8 m/s^2) = k(0.200 m), which gives us k = 14.7 N/m.

To find the unloaded length of the spring, we can use the equation x = mg/k, where x is the displacement, m is the mass, g is the acceleration due to gravity, and k is the force constant. Plugging in the values, we have x = (0.300 kg)(9.8 m/s^2)/(14.7 N/m) = 0.200 m.