a mass of 65 kg falls from rest 4.3m onto a spring with a stiffness coefficient of 62000 n/m. How far does the mass compress the spring?

To determine how far the mass compresses the spring, you can use the principle of conservation of mechanical energy.

First, let's calculate the potential energy (PE) that the mass gained by falling 4.3m. The potential energy is given by the equation:

PE = m * g * h

where m is the mass (65 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height (4.3 m).

PE = 65 kg * 9.8 m/s^2 * 4.3 m
= 2836.65 J

According to the conservation of mechanical energy, the potential energy gained by the mass is converted into potential energy stored in the spring.

The potential energy stored in a spring is given by the equation:

PE_spring = (1/2) * k * x^2

where k is the stiffness coefficient of the spring (62,000 N/m), and x is the compression distance.

We can rearrange the equation to solve for x:

x = sqrt((2 * PE_spring) / k)

Substituting the given values:

x = sqrt((2 * 2836.65 J) / 62,000 N/m)
= sqrt(0.09149113 m^2)
= 0.302 m

Therefore, the mass compresses the spring by approximately 0.302 meters (or 30.2 cm).