Not sure if I'm understanding mechanical energy correctly?

In summary, the potential energy of a 0.5 kg ball thrown vertically upward with an initial speed of 8 m/s, at a height of 2 m above the initial position is 9.8 J. The initial kinetic energy of the ball is also 9.8 J. The total mechanical energy at the maximum height is 16 J, and it remains constant due to the conservation of mechanical energy law.
  • #1
jle1092
13
0
A .5 kg ball is thrown vertically upward with an initial speed of 8 m/s. If the initial potential energy is taken as zero, find the following:
1. potential energy of the ball at a height of 2 m above the initial position
2. the initial kinetic energy of the ball
3. the total mechanical energy at the maximum height



PE= mgy
Potential Energy=(mass)(Gravity)(height)

KE(initial)+PE(initial)=KE(final)+PE(final)


1. So for the first one, this is how I solved for the potential energy:
PE=mgy
PE=(.5kg)(9.8m/s^2)(2m)
PE=9.8 J
I am pretty confident with how I solved this part of the problem.


2. The second question I had a little more trouble with.
I used:
KE(initial)+PE(initial)=KE(final)+PE(final), and plugged in what I knew:

KE(inital) + 0=0 + PE(final)

So since KE=PE I said that KE would also equal 9.8 J.


3. So if the ball had 9.8 J to begin with, and ended with 9.8 J, shouldn't this answer also be 9.8 J?



Thanks for the help.
 
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  • #2
jle1092 said:
1. So for the first one, this is how I solved for the potential energy:
PE=mgy
PE=(.5kg)(9.8m/s^2)(2m)
PE=9.8 J
I am pretty confident with how I solved this part of the problem.
Good!

2. The second question I had a little more trouble with.
I used:
KE(initial)+PE(initial)=KE(final)+PE(final), and plugged in what I knew:

KE(inital) + 0=0 + PE(final)

So since KE=PE I said that KE would also equal 9.8 J.
You need to calculate KE(initial) based on the speed that was given. (What's the definition of KE?)

Do not assume KE(final) is zero. No one said that 2 m was the maximum height of the ball.
 
  • #3
So would I set up the equation to :

KEi= (1\2mv^2) + PEf ?

If so, what do I use for PEf so that I can solve the equation?
 
  • #4
jle1092 said:
So would I set up the equation to :

KEi= (1\2mv^2) + PEf ?

If so, what do I use for PEf so that I can solve the equation?
For question 2 all you need is the definition of KE. (All they ask for is the initial KE.)

When solving question 3, then you'll need to use conservation of mechanical energy. Hint: It's a trick question. You shouldn't have to do any further calculations beyond what you already did.
 
  • #5
Doc Al said:
For question 2 all you need is the definition of KE. (All they ask for is the initial KE.)

When solving question 3, then you'll need to use conservation of mechanical energy. Hint: It's a trick question. You shouldn't have to do any further calculations beyond what you already did.

So, shouldn't the answer to the third one be 16?

Because:

PEi + KEi = PEf + KEf
0 + 16 = PEf + KEf


So it doesn't really matter what PEf and KEf are because they equal 16 combined, by the conservation of mechanical energy law?
 
  • #6
Exactly!
 
  • #7
Thank you for the help! :)
 

1. What is mechanical energy?

Mechanical energy refers to the energy that is possessed by an object due to its motion or position. It is a combination of both kinetic and potential energy.

2. How is mechanical energy different from other forms of energy?

Mechanical energy is different from other forms of energy because it is specifically related to the motion and position of an object. Other forms of energy, such as thermal or electrical energy, are not directly related to an object's motion or position.

3. Can mechanical energy be converted into other forms of energy?

Yes, mechanical energy can be converted into other forms of energy. For example, when a ball is dropped, its potential energy (due to its height) is converted into kinetic energy (due to its motion).

4. How is mechanical energy conserved in a system?

The total mechanical energy in a closed system remains constant. This means that energy cannot be created or destroyed, but it can be transformed from one form to another within the system.

5. How is the concept of mechanical energy used in real-world applications?

Mechanical energy is used in many real-world applications, such as in machines and vehicles. By utilizing different types of mechanical energy, such as potential energy in a spring or kinetic energy in a moving object, we can power various devices and perform work. It is also an important concept in understanding the laws of motion and how objects interact with each other.

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