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, we need to calculate the gravitational potential energy change as the block falls onto the spring. The work done by weight is equal to the change in potential energy.
The gravitational potential energy change is given by the equation:
ΔPE = m * g * h
where:
ΔPE is the change in potential energy
m is the mass of the block (395.0 g = 0.395 kg)
g is the acceleration due to gravity (approximated as 9.8 m/s^2)
h is the height the block falls (the compression of the spring = 0.29 m)
Plugging in the values, we have:
ΔPE = 0.395 kg * 9.8 m/s^2 * 0.29 m
To find the work done by the spring, we need to calculate the potential energy stored in the spring when it is compressed. The work done by the spring is equal to the change in potential energy.
The potential energy stored in a spring is given by the equation:
PE = 1/2 * k * x^2
where:
PE is the potential energy stored in the spring
k is the spring constant (252.0 N/m)
x is the compression of the spring (0.29 m)
Plugging in the values, we have:
PE = 1/2 * 252.0 N/m * (0.29 m)^2
To find the speed of the block just before it hits the spring, we can use the principle of conservation of energy. The initial potential energy of the block due to its height is transformed into kinetic energy just before it reaches the spring.
The initial potential energy can be calculated using the gravitational potential energy equation:
PE_initial = m * g * h
The final kinetic energy can be calculated using the equation:
KE_final = 1/2 * m * v^2
where:
m is the mass of the block (0.395 kg)
g is the acceleration due to gravity (9.8 m/s^2)
h is the height the block falls (0.29 m)
v is the final velocity of the block just before it hits the spring (unknown)
Equating the initial potential energy to the final kinetic energy, we have:
PE_initial = KE_final
m * g * h = 1/2 * m * v^2
Solving for v, we get:
v = sqrt(2 * g * h)
Plugging in the values, we have:
v = sqrt(2 * 9.8 m/s^2 * 0.29 m)
Now, you 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 hits the spring.
The energy in the spring at stopping has to be be equal to the KE when hitting the springl.
1/2 k (.29^2)=1/2 mass*V^2=work done by spring