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 work done by the block's weight, you need to calculate the gravitational potential energy before the block hits the spring.
The gravitational potential energy can be calculated using the formula:
Potential Energy = m * g * h
Where:
m = mass of the block = 395.0 g = 0.395 kg (mass should be in kilograms)
g = acceleration due to gravity = 9.8 m/s^2
h = height from which the block is dropped = 0.29 m (this is equal to the compression of the spring)
Plugging in the values:
Potential Energy = 0.395 kg * 9.8 m/s^2 * 0.29 m
Now, to find the work done by the block's weight, we know that work done is equal to the change in potential energy. Since the potential energy is being converted to work, the work done by the block's weight will be negative. This is because the block is losing potential energy.
Therefore, the work done by the block's weight = - Potential Energy.
To find the work done by the spring, you can make use of Hooke's Law, which states that the force exerted by a spring is proportional to its displacement. The formula is:
Force = -k * x
Where:
k = spring constant = 252.0 N/m
x = displacement of the spring = 0.29 m
Work done by the spring can be calculated using the formula:
Work = (1/2) * k * x^2
Now, to find the speed of the block just before it hits the spring, you can make use of the principle of conservation of mechanical energy. At the highest point of the block's fall, all of its potential energy is converted into kinetic energy. Therefore, the potential energy at that height can be equated to the kinetic energy just before the block hits the spring.
The formula for kinetic energy is:
Kinetic Energy = (1/2) * m * v^2
Where:
m = mass of the block = 0.395 kg
v = velocity/speed of the block just before hitting the spring
Setting the potential energy equal to the kinetic energy:
Potential Energy = Kinetic Energy
Plugging in the values:
0.395 kg * 9.8 m/s^2 * 0.29 m = (1/2) * 0.395 kg * v^2
You can solve this equation to find the value of v.