Question

A 2.3 kg box is sliding along a frictionless horizontal surface with a speed of 1.8 m/s when it encounters a spring.

If the spring has a spring constant of 400 N/m, calculate the maximum compression of the spring when the box comes to rest. Assume the spring behaves linearly.

Answer 1

The maximum compression of the spring when the box comes to rest is 19.2 cm.

Step-by-step explanation:

To find the maximum compression of the spring, we can use the principle of conservation of mechanical energy. The initial kinetic energy of the box is equal to the potential energy stored in the spring at maximum compression.

The initial kinetic energy can be calculated using the formula KE = 0.5 * mass * velocity^2. Plugging in the values, KE = 0.5 * 2.3 kg * (1.8 m/s)^2 = 3.708 J.

The potential energy stored in the spring can be calculated using the formula PE = 0.5 * k * compression^2, where k is the spring constant and compression is the maximum compression of the spring. Rearranging the formula, we get compression^2 = 2 * PE / k. Plugging in the values, compression^2 = 2 * 3.708 J / 400 N/m = 0.03708 m^2.

Taking the square root of both sides, we find that the maximum compression of the spring is compression = sqrt(0.03708 m^2) = 0.192 m, or 19.2 cm.