Question

Two identical 1.50kg masses are pressed against opposite ends of a spring of force constant 1.75N/cm, compressing the spring by 25.0cm from its normal length.

Find the maximum speed of each mass when it has moved free of the spring on a smooth, horizontal lab table.

Answer 1

To find the maximum speed of the masses when they have moved free of the spring, we can use the law of conservation of energy. By equating the potential energy stored in the spring to the final kinetic energy of the masses, we can solve for the maximum speed. The maximum speed of each mass is 20.91 m/s.

Step-by-step explanation:

To find the maximum speed of each mass when it has moved free of the spring, we need to apply the law of conservation of energy. The initial potential energy stored in the spring is equal to the final kinetic energy of the masses. The formula for the potential energy of a spring is given by U = (1/2)kx^2, where U is the potential energy, k is the force constant of the spring, and x is the displacement from the equilibrium position.

First, let's calculate the potential energy stored in the spring:

U = (1/2)(1.75 N/cm)(25.0 cm)^2 = 1093.75 J

Since the masses are identical, we can divide the potential energy equally between them:

1093.75 J / 2 = 546.875 J

Next, we equate the potential energy to the kinetic energy:

546.875 J = (1/2)mv^2

Solving for v, the maximum speed of each mass:

v = sqrt((2 * 546.875 J) / 1.5 kg) = 20.91 m/s