Mechanical Energy Problem Solutions

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Mechanical Energy Problems and Solutions

See examples of mechanical energy problems involving kinetic energy, potential energy, and the conservation of energy. Check your work with ours.

1. How much gravitational potential energy do you have when you lift a 15 N object 10 meters off the ground?

2. How much gravitational potential energy is in a 20 kg mass when 0.6 meters above the ground?

3. How much gravitational potential energy does a 35 kg boulder have when 30 meters off the ground?

4. How many times greater is an objects potential energy when three times higher?

If you need help on ratio problems click the link below:

Rule of Ones: analyzing equations to determine how other variables change

5.  How much kinetic energy does a 0.15 kg ball thrown at 24 m/s have?

6.  How many times greater is the kinetic energy of a ball that is going five times faster?

7.  How much kinetic energy does a 1.2 kg ball have the moment it hits the ground 3.5 meters below when it starts from rest?

 

I cancelled out the initial kinetic energy because:

  • KEi = ½ mvf2
  • KEi = (½)(3.5)(02) = 0 J

I cancelled out the final potential energy because:

  • PEf = mghf
  • PEf = (3.5)(9.8)(0) = 0 J
ME Problem 7 Solution

8.  How fast is a 1.2 kg ball traveling the moment it hits the ground 3.5 meters below when it starts from rest?

I cancelled out the initial kinetic energy because:

  • KEi = ½ mvf2
  • KEi = (½)(3.5)(02) = 0 J

I cancelled out the final potential energy because:

  • PEf = mghf
  • PEf = (3.5)(9.8)(0) = 0 J

(Note: In many of these problems I could cancel out mass but did not since it was provided)

Since I did not cancel out mass I could answer the following questions if asked:

  • How much mechanical energy did you have at the beginning? (41.6 J)
  • How much kinetic energy did you have at the beginning? (0 J)
  • How much potential energy did you have at the beginning? (41.6 J)
  • How much potential energy do you have at the end? (0 J)

If I cancelled out mass in my work it would not show the actual initial potential energy since PEi = mgh and not just gh.

 

ME Problem 8 Solution

9.  A 3.5 kg ball fell from a height of 12 meters.  How fast is it traveling when its still 5 meters off the ground?

I cancelled out the initial kinetic energy because:

  • KEi = ½ mvf2
  • KEi = (½)(3.5)(02) = 0 J

10. An 85kg roller coaster cart is traveling 4 m/s at the top of a hill 50 meters off the ground.  How fast is it traveling at top of a second hill 20 meters off the ground?

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