A 390.0 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 0.15 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 work done by the block's weight, we can use the equation:

Work = Force x Distance x cos(θ)

Where Force is the weight of the block, Distance is the distance it moves, and θ is the angle between the force and the direction of motion. Since the block is dropped vertically, the angle is 0 degrees, and cos(0) = 1.

Weight = mass x acceleration due to gravity
Weight = 0.390 kg x 9.8 m/s^2 = 3.822 N

Distance = compression of the spring = 0.15 m

Work done by weight = 3.822 N x 0.15 m x cos(0) = 0.5733 J

So, the work done by the block's weight is 0.5733 Joules.

To find the work done by the spring, we can use the equation:

Work = 0.5 x k x x^2

Where k is the spring constant and x is the displacement from the equilibrium position (compression of the spring).

Work done by the spring = 0.5 x 252 N/m x (0.15 m)^2 = 1.782 J

So, the work done by the spring is 1.782 Joules.

To find the speed of the block just before it hit the spring, we can use the principle of conservation of energy. The potential energy when the block is dropped is converted to the kinetic energy just before hitting the spring.

Potential energy = m x g x h
Kinetic energy = 0.5 x m x v^2

Where m is the mass, g is the acceleration due to gravity, h is the height from which the block is dropped, and v is the velocity/speed of the block just before hitting the spring.

Potential energy = 0.390 kg x 9.8 m/s^2 x h
Kinetic energy = 0.5 x 0.390 kg x v^2

Since potential energy is converted to kinetic energy,

0.5 x 0.390 kg x v^2 = 0.390 kg x 9.8 m/s^2 x h

Simplifying,

0.5 x v^2 = 9.8 m/s^2 x h

v^2 = 2 x 9.8 m/s^2 x h

v^2 = 19.6 m/s^2 x h

Taking the square root of both sides,

v = sqrt(19.6 m/s^2 x h)

Given that the height from which the block is dropped is not provided, we cannot calculate the exact speed of the block just before it hit the spring without this information.