a basketball of mass 0.5 kg is dropped from restfrom a height of 1.34m.it rebounds to a height of 0.6m. how much mechanicalenergy was lost during the collision with the floor?
To calculate the mechanical energy lost during the collision with the floor, we need to determine the initial mechanical energy before the ball was dropped and compare it to the total mechanical energy after the ball rebounds.
The mechanical energy of an object consists of its potential energy (PE) due to its height and its kinetic energy (KE) due to its motion. The sum of these two forms of energy is called the mechanical energy (ME) and is given by the equation:
ME = PE + KE
Let's break down the calculation step by step:
Step 1: Calculate the initial potential energy (PEi):
The potential energy when the ball is initially dropped can be calculated using the formula:
PEi = m * g * hi
where m is the mass of the basketball (0.5 kg), g is the acceleration due to gravity (9.8 m/s^2), and hi is the initial height (1.34 m).
PEi = 0.5 kg * 9.8 m/s^2 * 1.34 m
Step 2: Calculate the final potential energy (PEf):
At the rebound height, the potential energy can be calculated using the same formula but with the final height (hf = 0.6 m).
PEf = m * g * hf
PEf = 0.5 kg * 9.8 m/s^2 * 0.6 m
Step 3: Calculate the initial kinetic energy (KEi):
The initial kinetic energy of the ball right before it hits the ground is zero since it is dropped from rest.
KEi = 0
Step 4: Calculate the final kinetic energy (KEf):
The final kinetic energy after the rebound can be calculated using the formula:
KEf = 0.5 * m * v^2
Since we don't know the velocity (v) directly, we can use the conservation of mechanical energy principle. The mechanical energy before the collision is equal to the mechanical energy after the collision (assuming no other external forces are acting, like air resistance). So the kinetic energy after the rebound is the same as the initial kinetic energy before the drop.
KEf = KEi (by conservation of mechanical energy)
Step 5: Calculate the mechanical energy lost:
The mechanical energy lost during the collision can be determined by subtracting the final mechanical energy (MEf = KEf + PEf) from the initial mechanical energy (MEi = KEi + PEi).
MElost = MEi - MEf
MElost = (PEi + KEi) - (PEf + KEf)
After calculating the values from the previous steps, you can substitute them into the equation to find the mechanical energy lost during the collision.