Kinetic and Potential Energy

In summary, a ball is thrown upward and at a height of 10 meters above the ground, it has a potential energy of 50 Joules and is moving upward with a kinetic energy of 50 Joules. Due to negligible air friction, the maximum height reached by the ball is approximately 20 meters.
  • #1
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A ball is thrown upward. At a height of 10 meters above the ground, the ball has a potential energy of 50 Joules (with the potential energy equal to zero at ground level) and is moving upward with a kinetic energy of 50 Joules. Air friction is negligible. The maximum height 'h' reached by the ball is most nearly
1. h = 30 m
2. h = 50 m
3. h = 10 m
4. h = 20 m
5. h = 40 m
(all answers are approximate)

haha, I think I finally figured it out, but let me make sure if I'm right. I'm thinking that since both the Potential Energy and Kinetic energy are equal, that means that the ball is half way through it's path, right? So that should mean that the height is 20 meters.

Am I correct?
 
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  • #2
A little more precise way of saying this (as opposed to "yep"!)
is that you are given that the total energy is 100 Joules. The ball will be at its highest point when its speed is 0 so all the energy is converted to potential energy: mgh= 100. Since the potential energy at 10 meters above the ground was 50, you know that mg(10)= 50 or that mg= 5. Thus mgh= = 5h= 100 so h= 20.

Or- since the kinetic energy and potential energy are the same, when there is no kinetic energy the potential energy will be twice as great. Twice the potential energy, twice the height!

Or- in the succinct words of enigma: "Yep"!
 
  • #3


Yes, you are correct! Since the potential energy and kinetic energy are equal at a height of 10 meters, that means the ball is halfway through its path and will reach a maximum height of 20 meters. This is because as the ball is thrown upward, it gains potential energy and loses kinetic energy due to gravity. At the highest point, all of the kinetic energy is converted into potential energy. So, the maximum height reached by the ball is 20 meters.
 

1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is directly proportional to the mass and velocity of the object, meaning that the greater the mass and velocity, the greater the kinetic energy.

2. What is potential energy?

Potential energy is the energy an object possesses due to its position or state. It is stored energy that can be converted into other forms, such as kinetic energy, when the object is in motion.

3. What is the relationship between kinetic and potential energy?

Kinetic and potential energy are two forms of mechanical energy. The total mechanical energy of a system is the sum of its kinetic and potential energy. As an object moves, it converts potential energy into kinetic energy and vice versa.

4. How is kinetic energy calculated?

The formula for calculating kinetic energy is KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity. The unit of kinetic energy is joules (J).

5. What are some real-life examples of kinetic and potential energy?

An object falling from a height has potential energy that is converted into kinetic energy as it accelerates towards the ground. A car moving at a high speed has kinetic energy, while a stretched spring has potential energy. Other examples include a swinging pendulum, a rollercoaster, and a bouncing ball.

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