A brick with a mass of 0.400kg is pressed against a vertical spring with force constant k=500
N(m^-1) such that the spring is compressed 0.200m. When the brick is released, how high does it rise from this position? (the brick and the spring are not attached. The spring has negligible mass.)
To find the height the brick will rise to when released from the compressed spring, we need to consider the conservation of mechanical energy.
First, let's calculate the potential energy stored in the compressed spring. The potential energy stored in a spring can be calculated using the formula:
Elastic potential energy (PE) = (1/2)kx^2
where k is the force constant of the spring and x is the displacement from the equilibrium position. In this case, the displacement is given as 0.200m and the force constant is 500 N/m.
PE = (1/2) * 500 N/m * (0.200m)^2
PE = 10 J
Next, we need to find the gravitational potential energy gained by the brick as it rises. The change in gravitational potential energy (ΔPE) is given by the formula:
ΔPE = m * g * h
where m is the mass of the brick, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height gained.
Since the brick is not attached to the spring and the spring has negligible mass, we can consider the gravitational potential energy gained by the brick to be equal to the potential energy stored in the spring.
ΔPE = 10 J
Now, we can rearrange the formula to solve for h:
ΔPE = m * g * h
h = ΔPE / (m * g)
Substituting the values:
h = 10 J / (0.400 kg * 9.8 m/s^2)
h ≈ 25.5 m
Therefore, the brick will rise approximately 25.5 meters from the compressed position when released from the spring.