Help Total mechanical energy question

In summary, the question asks for the speed of a 1 kg rock thrown upwards at 20 m/s from a 30 m building, just before it hits the ground. Total mechanical energy is conserved, so the mechanical energy at the start must be equal to the mechanical energy at the end, which includes gravitational potential energy and kinetic energy. Therefore, the speed of the rock when it hits the ground can be calculated using the total mechanical energy equation, which is equal to the sum of gravitational potential energy and kinetic energy. The speed at the instant just before impact is determined by the conservation of mechanical energy principle.
  • #1
adv
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[SOLVED] Help! Total mechanical energy question:)

Q. Suppose you are standing on a 30 m building and throw a 1 kg rock upwards at 20 m/s. Knowing that total mechanical energy is conserved, calculate the speed of the rock when it hits the ground.


Total Mechanical Energy equation:

Etotal = Egravitational + Ekinetic
Et = Eg + Ek
= mgh + ½mv2


What is the speed of the rock when it hits the ground? Well, the gravitational potential energy would be 0, if the reference point is the ground, yes? The upwards motion of the rock has thrown me off:confused:
 
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  • #2
Correct me if I'm wrong, but when the rock hits the ground, wouldn't the speed be zero? It's not moving.
 
  • #3
adv said:
Correct me if I'm wrong, but when the rock hits the ground, wouldn't the speed be zero? It's not moving.
The problem is asking you to determine the rock's speed at the instant just before it hits the ground.
Since total mechanical energy is conserved, the mechanical energy that the rock has at the instant it leaves the thrower's hand must be equal to its total mechanical energy at the instant just before it hits the ground.
 

1. What is total mechanical energy?

Total mechanical energy is the sum of the kinetic energy and potential energy of a system. Kinetic energy is the energy of motion, while potential energy is the energy stored in an object due to its position or configuration.

2. How is total mechanical energy calculated?

Total mechanical energy is calculated by adding the kinetic energy and potential energy of a system. 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 formula for potential energy varies depending on the type of potential energy (such as gravitational potential energy or elastic potential energy).

3. What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, only transferred from one form to another. This means that in a closed system, the total amount of energy remains constant.

4. Can total mechanical energy be negative?

Yes, total mechanical energy can be negative. This occurs when the potential energy is greater than the kinetic energy. For example, if an object is at rest at the top of a hill, it has zero kinetic energy but a negative potential energy due to its position.

5. How does friction affect total mechanical energy?

Friction converts some of the kinetic energy of a system into heat, resulting in a decrease in total mechanical energy. This is why objects in motion eventually come to a stop - the energy is being transferred to the surrounding environment as heat.

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