A block of mass 4.253 kg is released on
the track at a height 5.52 m above the level surface. It slides down the track and makes a head-on elastic collision with a block of mass 17.012 kg, initially at rest. The acceleration of gravity is 9.8 m/s2 . Calculate the height to which the block
with mass 4.253 kg rises after rebounding from the collision.
To determine the height to which the block with a mass of 4.253 kg rises after rebounding from the collision, we can utilize the principle of conservation of mechanical energy.
First, we need to calculate the potential energy of the block before the collision when it is at a height of 5.52 m. The potential energy (PE) is given by the formula:
PE = m * g * h
Where:
m = mass of the block (4.253 kg)
g = acceleration due to gravity (9.8 m/s²)
h = height (5.52 m)
PE = 4.253 kg * 9.8 m/s² * 5.52 m
PE ≈ 230.64 Joules
Next, since the collision is elastic, the total mechanical energy (sum of kinetic and potential energy) is conserved. Therefore, the total mechanical energy before the collision (before the block reaches its maximum height) is equal to the total mechanical energy after the collision (at the maximum height).
At the maximum height, the block's kinetic energy will be zero, so the total mechanical energy is equivalent to the potential energy.
To calculate the maximum height, we need to find the potential energy at that height. We'll use the formula:
PE = m * g * h
Where:
m = mass of the block (4.253 kg)
g = acceleration due to gravity (9.8 m/s²)
h = maximum height (unknown)
Rearranging the formula, we have:
h = PE / (m * g)
Substituting the known values:
h = 230.64 J / (4.253 kg * 9.8 m/s²)
h ≈ 5.387 m
Therefore, the block with a mass of 4.253 kg rises to a height of approximately 5.387 meters after rebounding from the collision.