A ball mass 0.2kg is dropped from the height of 20m on the impact with ground lose 30j of energy calculate the height it reachon the rebound
[(0.2 * g * 20) - 30] / (0.2 * g) = ? m
To calculate the height the ball reaches on the rebound, we need to use the law of conservation of energy.
According to the law of conservation of energy, the total mechanical energy of a system remains constant unless acted upon by an external force. In this case, the system is the ball.
The initial mechanical energy of the ball when it is dropped from a height of 20m is given by:
Initial mechanical energy = Potential energy = mass * acceleration due to gravity * height
= 0.2kg * 9.8m/s^2 * 20m
= 39.2 Joules
Since the ball loses 30 Joules of energy on impact with the ground, the final mechanical energy can be calculated as:
Final mechanical energy = Initial mechanical energy - Energy loss
= 39.2 Joules - 30 Joules
= 9.2 Joules
Now, to find the height the ball reaches on the rebound, we can use the final mechanical energy and the potential energy formula:
Final mechanical energy = Potential energy = mass * acceleration due to gravity * height_rebound
Rearranging the formula, we can solve for the height_rebound:
height_rebound = Final mechanical energy / (mass * acceleration due to gravity)
= 9.2 Joules / (0.2kg * 9.8m/s^2)
= 47.959m
Therefore, the height the ball reaches on the rebound is approximately 47.96 meters.