Question

A 10 kg box is dropped outside a window onto a vertical spring located 6 m below. The spring constant for the spring is 500 N/m. If the average air resistance friction force for the entire drop is 80 N, then calculate the amount of compression in the spring

Answer 1

The amount of compression in the spring is approximately 0.036 meters.

Step-by-step explanation:

To find the amount of compression in the spring, we first need to calculate the total force acting on the box as it falls. The force due to gravity can be calculated using the equation F = mg, where m is the mass of the box and g is the acceleration due to gravity. Given that the mass of the box is 10 kg and the acceleration due to gravity is 9.8 m/s², the force due to gravity is 10 kg * 9.8 m/s² = 98 N.

Next, we subtract the average air resistance friction force from the force due to gravity. So, the net force acting on the box is 98 N - 80 N = 18 N.

The force exerted by the spring can be calculated using Hooke's Law, which states that the force exerted by a spring is proportional to the compression or extension of the spring. The equation for Hooke's Law is F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the compression or extension of the spring. Rearranging the equation, we have x = -F / k.

Plugging in the values, we have x = -18 N / 500 N/m = -0.036 m.