A 330.0 g block is dropped onto a vertical spring with a spring constant k = 234.0 N/m. The block becomes attached to the spring, and the spring compresses 0.26 m before momentarily stopping.
A) While the spring is being compressed, what what is the change in the objects gravitational potential energy?
B) What is the change in the objects spring potential energy?
C) What was the speed of the block just before it hit the spring?
To answer these questions, we need to understand the concept of potential energy and the formulas associated with it.
A) The change in the object's gravitational potential energy can be calculated using the formula:
ΔUg = mgh
Where:
ΔUg is the change in gravitational potential energy
m is the mass of the object (330.0 g = 0.330 kg)
g is the acceleration due to gravity (approximately 9.8 m/s²)
h is the change in height, which is the distance the block fell before hitting the spring.
To find h, we need to use the concept of conservation of mechanical energy. The initial potential energy of the block (mgΔh) will be converted into the potential energy of the spring (∆Uspring) when it momentarily stops.
B) The change in the object's spring potential energy can be calculated using the formula:
ΔUspring = 1/2(kx²)
Where:
ΔUspring is the change in spring potential energy
k is the spring constant (234.0 N/m)
x is the deformation or compression of the spring when the block momentarily stops (0.26 m)
C) To find the speed of the block just before it hits the spring, we need to use the principle of conservation of mechanical energy. The initial potential energy (mgΔh) of the block should be converted into the kinetic energy right before it hits the spring, which can be calculated using the formula:
KE = 1/2mv²
Where:
KE is the kinetic energy
m is the mass of the object (0.330 kg)
v is the speed of the block just before it hits the spring.
Now, let's calculate each of these values step by step:
A) ΔUg = mgh
ΔUg = (0.330 kg) * (9.8 m/s²) * h
B) ΔUspring = 1/2(kx²)
ΔUspring = 1/2 * (234.0 N/m) * (0.26 m)²
C) KE = 1/2mv²
Find v.
To find h, we need to know the distance the block fell before hitting the spring.