A ball of mass 1.2kg and a volume of 35cm cubed is dropped from a height of 2m. Determine the height to which this ball will bounce.
If the collision with the ground is perfectly elastic it will bounce back up to 2m. Otherwise you have to know how squishy the collision was.
The density of the ball, 34 g/cm^3, is higher than that of any known material outside a star. Even uranium has a density about half that.
Did you make up that question? Perhaps someone is playing a practical joke with this question.
If you dropped that ball on concrete, it would probably leave send pieces of concrete flying, leave a crater, and bounce poorly.
drwls- so the answer cannot be determined?
Correct. An experiment would be needed to establish the fractional energy loss per bounce.
To determine the height to which the ball will bounce, we need to consider the conservation of mechanical energy.
The ball is initially at a height of 2 meters, so it has potential energy given by the equation:
Potential energy = mass * acceleration due to gravity * height
We can calculate the potential energy using the given mass and height:
Potential energy = 1.2 kg * 9.8 m/s^2 * 2 m
= 23.52 Joules
When the ball reaches its highest point after bouncing, all of its potential energy is converted into kinetic energy. At this highest point, the ball has no height, so all the potential energy is transformed into kinetic energy:
Kinetic energy = 23.52 Joules
The kinetic energy of the ball can be calculated using the equation:
Kinetic energy = 0.5 * mass * velocity^2
Since we know the mass of the ball (1.2 kg), we can rearrange the equation to solve for the velocity:
velocity = √(2 * kinetic energy / mass)
Plugging in the values we know:
velocity = √(2 * 23.52 Joules / 1.2 kg)
= √(39.2 m^2 / s^2)
= 6.26 m/s
Now, we can use the principle of conservation of mechanical energy to find the height to which the ball will bounce. At the highest point after bouncing, the total mechanical energy (kinetic + potential energy) will be equal to the initial potential energy.
Total mechanical energy = 23.52 Joules
Using the equation for potential energy, we can calculate the height to which the ball will bounce:
Potential energy = mass * acceleration due to gravity * height
23.52 Joules = 1.2 kg * 9.8 m/s^2 * height
height = 23.52 Joules / (1.2 kg * 9.8 m/s^2)
= 1.92 meters
Therefore, the ball will bounce to a height of approximately 1.92 meters.