A ball is dropped from a height of 10 meter.If the energy of the ball reduces by 40% after striking the ground, how much high can the ball bounce back?
well, since potential energy is mgh, and m and g do not change, I'd say the height is reduced by 40%, or 6m.
To determine how high the ball can bounce back, we need to understand the concept of energy conservation.
When the ball is dropped from a height of 10 meters, it possesses potential energy due to its position. As it falls, this potential energy is converted into kinetic energy, which is the energy of motion.
When the ball strikes the ground, some of its kinetic energy is converted into other forms, such as heat and sound, leading to a reduction in its energy. The question states that the energy reduces by 40% after striking the ground.
To find out how high the ball can bounce back, we need to calculate the rebound energy. We know that 60% of the original energy remains after the collision with the ground, as it has reduced by 40%.
Now, let's assume that the ball bounces back to a height of 'h' meters. At this height, the ball would again have potential energy due to its position.
According to the principle of energy conservation, the rebound energy should be equal to the potential energy at the maximum height.
So, we can set up the equation:
60% of the original energy = Potential energy at maximum height
Potential energy at maximum height = mass * gravitational acceleration * height
Since the mass of the ball cancels out in this calculation, we can simplify the equation as follows:
0.6 * original energy = gravitational acceleration * h
Now, we need to know the value of the gravitational acceleration, which is approximately 9.8 m/s² on Earth.
Plugging in the values, we have:
0.6 * original energy = 9.8 * h
We can rearrange this equation to solve for 'h':
h = (0.6 * original energy) / 9.8
By calculating this expression, we can determine how high the ball would bounce back based on the given reduction in energy.