A 395.0 g block is dropped onto a vertical spring with a spring constant k = 252.0 N/m. The block becomes attached to the spring, and the spring compresses 0.29 m before momentarily stopping. While the spring is being compressed, what work is done by the block's weight?

What work is done by the spring?
What was the speed of the block just before it hit the spring?

To find the answers to these questions, we need to understand the concepts of work, potential energy, and conservation of energy.

1. What work is done by the block's weight?
The work done by the block's weight can be calculated using the formula: Work = Force x Distance x cos(theta), where theta is the angle between the force and the displacement. In this case, the block is dropped vertically, so the angle between the weight (force) and the displacement is 0 degrees, and cos(0) = 1. Thus, the work done by the block's weight is given by: Work = Force x Distance = mgd, where m is the mass of the block, g is the acceleration due to gravity, and d is the distance the block falls. Plugging in the values: m = 395.0 g = 0.395 kg, g = 9.8 m/s^2, and d = 0.29 m, we can calculate the work done by the block's weight.

2. What work is done by the spring?
The work done by the spring can be calculated using the formula: Work = (1/2)kx^2, where k is the spring constant and x is the compression or extension of the spring. In this case, the spring compresses by 0.29 m, so we can substitute these values into the formula to calculate the work done by the spring.

3. What was the speed of the block just before it hit the spring?
To find the speed of the block just before it hit the spring, we can use the principle of conservation of mechanical energy. Before the block hits the spring, it only has potential energy due to its height above the ground. This potential energy is given by: Potential Energy = mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the initial height. The initial height is not given in the problem statement, but we can assume it is the same as the distance the spring compresses, which is 0.29 m. The potential energy is then converted into kinetic energy just before the block hits the spring. The kinetic energy is given by: Kinetic Energy = (1/2)mv^2, where v is the speed of the block just before it hits the spring. Equating the initial potential energy to the final kinetic energy, we can solve for v.

By following these steps, we can calculate the work done by the block's weight, the work done by the spring, and the speed of the block just before it hit the spring.