A basketball player throws a 1.2 kg ball 15 meters into the air. What is the increase in potential energy? What is the work done by the player?
Is the answer the same for each, because I'm getting the same answer but I feel like something is wrong...
176J
PE = mgh = 1.2 * 9.8 * 15 = 176.4J
you are correct
work = energy, since both are in Joules
Well, well, well, it seems we have a physics question! Let me juggle with the numbers for you.
The increase in potential energy is indeed equal to the work done by the player. So, if you got 176J for both, congratulations! You're on the right track, my friend.
Think of it this way: the player had to exert a force to lift the ball against gravity, which caused the ball to gain potential energy. That potential energy is then converted into kinetic energy as the ball is thrown into the air.
So, don't worry, there's nothing wrong with your calculations. It appears that you've mastered the art of physics humor, too!
To calculate the increase in potential energy, you can use the formula:
Potential Energy = mass * acceleration due to gravity (9.8 m/s²) * height
Plugging in the values:
Potential Energy = 1.2 kg * 9.8 m/s² * 15 m = 176.4 Joules
So the increase in potential energy is 176.4 Joules.
Now, let's calculate the work done by the player to throw the ball. The formula for work is:
Work = force * distance
In this case, the force exerted by the player is equal to the weight of the ball, which can be calculated using the formula:
Force = mass * acceleration due to gravity
Plugging in the values:
Force = 1.2 kg * 9.8 m/s² = 11.76 N
Since the ball is thrown vertically upwards, the force exerted by the player is in the opposite direction to the displacement. Therefore, we need to take the negative sign to indicate that the work is done against the force of gravity.
Work = -11.76 N * 15 m = -176.4 Joules
So, the work done by the player is -176.4 Joules.
It appears that you've made a calculation error somewhere, as the increase in potential energy and the work done by the player should have the same magnitude but opposite signs. The correct answers should be -176.4 Joules for the work done by the player and 176.4 Joules for the increase in potential energy.
To calculate the increase in potential energy, we can use the formula:
Potential Energy = mass * gravitational acceleration * height
In this case, the mass of the ball is 1.2 kg, and the height it is thrown is 15 meters. The gravitational acceleration on Earth is approximately 9.8 m/s².
So the increase in potential energy is:
Potential Energy = 1.2 kg * 9.8 m/s² * 15 m
= 176.4 Joules (J)
Now let's calculate the work done by the player. The work done can be found using the formula:
Work = force * distance
To find the force, we can use Newton's second law:
Force = mass * acceleration
Since the ball is thrown vertically, there is no horizontal force acting on it, so the only force we consider is the gravitational force. Thus, the acceleration is the gravitational acceleration, which is 9.8 m/s².
Now, the distance is the height the ball is thrown, which is 15 meters.
So the work done by the player is:
Work = mass * acceleration * distance
= 1.2 kg * 9.8 m/s² * 15 m
= 176.4 Joules (J)
As you can see, the increase in potential energy and the work done by the player have the same value of 176.4 J. This is because the player used their force to overcome the gravitational force, resulting in the ball gaining potential energy. So it is expected to get the same answer for both calculations.