Question

İn a situation where the kinetic friction force in air is 10 N, a stationary block with a mass of 2 kg falls from a height y onto a spring with spring constant k = 400 N/m. Since the maximum compression in the spring is 3 m, find the height y. Solve it using the energy method

Answer 1

The height y is approximately 2.91 meters.

Step-by-step explanation:

To find the height y when a stationary block falls onto a spring, we can use the principle of conservation of mechanical energy. At the highest point of the fall, the block has only potential energy, which is converted to elastic potential energy when it compresses the spring.

The equation that relates potential energy and spring potential energy is

mgh = (1/2)kx^2,

where m is the mass of the block, g is the acceleration due to gravity, h is the height, k is the spring constant, and x is the maximum compression of the spring. In this case, the mass of the block is 2 kg, the spring constant is 400 N/m, and the maximum compression is 3 m. Substituting these values and solving for h, we get:

h = \frac{(1/2)kx^2}{mg}

h = \frac{(1/2)(400 N/m)(3 m)^2}{(2 kg)(9.8 m/s^2)}

h \approx 2.91 m

Therefore, the height y is approximately 2.91 meters.