Mechanical Energy Homework: Find E of 0.13 kg Ball at 5.00 m

In summary, the conversation discusses a homework question about calculating the mechanical energy of a ball at a certain point above the ground. After attempting the solution using the kinetic energy equation and receiving a different answer than expected, it is revealed that the potential energy of the ball should also be included in the calculation. The final answer is determined to be 32.4 J.
  • #1
cybernerd
27
0

Homework Statement



A 0.13 kg ball moves at a rate of 20.0 m/s at the point where it is 5.00 m above the ground. How much mechanical energy does the ball have with respect to the ground?

Homework Equations



Ek = 1/2mv^2

The Attempt at a Solution



Ek = 1/2mv^2
Ek = 1/2(0.13kg)(20m/s)^2
E = 26 J

The assignment says my answer should be 32.4 J.
Obviously, I am doing something wrong, but I'm not sure how to incorporate the "with respect to the ground" bit into my equations.

Somebody offer me some guidance, please?
 
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  • #2
I can't comment on WHY this is so.. but apparently.. the answer includes the potential energy of the ball as well

= mass x gravity x height

= .13 * 9.80 * 5m = 6.37J

26 J + 6.37J = 32.4J



Not really helping but I'm not familiar with mechanical energy...
 
  • #3
Hmm...that is strange...I really don't like the way that the question is worded.

But that did help, thank you.
 

FAQ: Mechanical Energy Homework: Find E of 0.13 kg Ball at 5.00 m

What is mechanical energy?

Mechanical energy is the sum of potential energy and kinetic energy of an object. Potential energy is the energy that an object has due to its position or configuration, while kinetic energy is the energy an object has due to its motion.

How do you calculate mechanical energy?

Mechanical energy can be calculated by adding the potential energy and kinetic energy of an object. The formula for mechanical energy is: E = PE + KE. In this case, we need to find the potential energy and kinetic energy of the 0.13 kg ball at 5.00 m.

How do you find the potential energy of an object?

The potential energy of an object can be calculated by multiplying the mass of the object by the acceleration due to gravity (9.8 m/s^2) and the height of the object. The formula for potential energy is: PE = mgh. In this case, we need to plug in the values for the ball's mass, height (5.00 m), and acceleration due to gravity.

How do you find the kinetic energy of an object?

The kinetic energy of an object can be calculated by multiplying half of the mass of the object by its velocity squared. The formula for kinetic energy is: KE = 1/2mv^2. In this case, we need to plug in the values for the ball's mass and velocity (which is not given in the question).

How can I check if my calculation for mechanical energy is correct?

To check if your calculation for mechanical energy is correct, you can use the conservation of energy principle, which states that energy cannot be created or destroyed, only transferred from one form to another. This means that the total mechanical energy of the ball before and after it reaches 5.00 m should be the same. You can also double check your calculations and make sure you have used the correct units for mass, height, and velocity.

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