Calculating Work Done on a Basketball Dropped from 5m

In summary, a basketball with a mass of 0.56 kg is dropped from a height of 5 m and bounces back up to a maximum height of 4.3 m. The work done by the ground on the ball during the time it is in contact with it can be calculated using the equation W = -ΔUg, where Ug = mgh. After solving, the work done by the ground is found to be -3.92 J, indicating that the ground does negative work on the ball. However, there was a signage error in the calculation as the equation used was for work done by gravity, not the ground. The correct equation to use for work done by the ground is W = -Δ
  • #1
Fatima Hasan
319
14

Homework Statement


A basketball with a mass of 0.56 kg drops from a height of 5 m and bounces off the floor back up to a maximum height of 4.3 m .Find the work done on the ball by the ground during the time the ball is in contact with it.

Homework Equations


W = - Δ Ug
Ug = mgh

The Attempt at a Solution


ΔUg = mghƒ - mghι
= 0.56*10*4.3 - 0.56*10*5 = - 3.92 J
W= - Ug = 3.92 J
Can somebody check my answer please ?
Thanks for your help.
 
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  • #2
The magnitude of the work done by the ground is correct, however you have a signage error because you incorrectly applied the equation for work done by the ground. The formula you used is for the work done by gravity. What equation should you be using for work done by the ground, which is work done by a non conservative force?
 

Related to Calculating Work Done on a Basketball Dropped from 5m

1. How do you calculate the work done on a basketball dropped from 5m?

The work done on an object is equal to the force applied multiplied by the distance traveled in the direction of the force. In this case, the force is the gravitational force, which is equal to the mass of the basketball multiplied by the acceleration due to gravity (9.8 m/s^2). The distance the ball travels is 5m, so the calculation would be: Work = Force x Distance = (mass x 9.8) x 5 = 49 x mass.

2. What is the unit of measurement for work?

The unit of measurement for work is the joule (J), which is equal to the force of one newton (N) applied over a distance of one meter (m).

3. Can you calculate the work done on a basketball without knowing its mass?

No, the mass of the basketball is a necessary component in calculating the work done. Without knowing the mass, we cannot determine the force applied by gravity.

4. Is the work done on a basketball the same as its kinetic energy when it hits the ground?

No, the work done on the basketball is the amount of energy transferred to the ball by gravity as it falls. The kinetic energy of the ball when it hits the ground is equal to the work done on it, but it also includes the potential energy it had at the top of the drop.

5. Can you calculate the work done on a basketball dropped from 5m on other planets or moons?

Yes, the work done on an object depends on the force applied and the distance traveled, so it can be calculated for any location with a known gravitational force and distance. However, the mass of the object may vary on different planets or moons, which would affect the calculation.

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