Mechanical energy- Falling rock

In summary, the conversation discusses finding the final velocity of a falling rock using the conservation of mechanical energy law. The solution involves finding the square root of 2 multiplied by the acceleration due to gravity and the difference in height between the starting point and the ground. The solution is 7.7m/s.
  • #1
fiziks09
28
0

Homework Statement


If the original height of a falling rock is y1 = h = 3.0m; calculate the rock's speed just before it hits ground.

Homework Equations


From conservation of mechanical energy law

1/2mv1^2 + mgy1 = 1/2mv2^2 + mgy2

The Attempt at a Solution


I think I'm supposed to find v2 i.e final velocity

v1 = 0 (from rest)
y1 = 3
Applying the formula stated above we find that the m's cancel out giving

v2 = sqrt(2g(y2 - y1))
= sqrt(2 x 9.8(3 - 0))
= sqrt(58.8)
= 7.7m/s

Please i want to know if my solution is correct. I'm not sure if it is right to take y2 as zero. Any help will be very much appreciated
 
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  • #2
Perfectly done!
 
  • #3
Okay; thanks for verifying !
 

1. What causes a falling rock to have mechanical energy?

A falling rock has mechanical energy because of its motion and position. As it falls, it gains kinetic energy due to its velocity, and potential energy due to its height above the ground.

2. How is the amount of mechanical energy in a falling rock determined?

The amount of mechanical energy in a falling rock is determined by its mass, velocity, and height. The higher the mass and/or velocity, and the greater the height, the more mechanical energy the rock will have.

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

Yes, mechanical energy can be converted into other forms of energy. When a falling rock hits the ground, its mechanical energy is converted into sound and thermal energy due to the impact.

4. What factors affect the rate at which a falling rock loses its mechanical energy?

The primary factor that affects the rate at which a falling rock loses its mechanical energy is air resistance. The more air resistance the rock encounters, the more kinetic energy it will lose as it falls. Other factors such as the shape and density of the rock can also affect the rate of energy loss.

5. What happens to the mechanical energy of a falling rock when it reaches the ground?

When a falling rock reaches the ground, its mechanical energy is mostly converted into other forms of energy, such as sound and thermal energy. However, some energy may also be retained in the form of deformation of the ground or the rock itself.

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