# A .5 kg rock is dropped from a height of 20 meters into a pail

• Sheldinoh
In summary, the question is about finding the rise in temperature of a 0.5 kg rock and a 0.6 kg water when the rock is dropped from a height of 20 meters into the water. The specific heat of the rock is 1480 and the specific heat of the water is 4186. The correct equation to use is mgh + mcT = mcT, where m is the mass and c is the specific heat. Both the rock and water will gain heat energy from the potential energy, resulting in a rise in temperature for both.
Sheldinoh
My Physics teacher gave us a quiz problem and I don't understand it really how he got his answer. Can you please give me your answer and an explanation for the answer Thanks. Here is the question:

A .5 kg rock is dropped from a height of 20 meters into a pail containing .6 kg of water. The rock has a specific heat of 1480 and the water has a specific heat of 4186. What is the is the rise in temperature of the rock and water ?

Show what you have tried already.

I think it is:
mgh(energy of fall ) = mcT + mcT

My teacher says its:
mgh + mcT = mcT

.In terms of energy changes PE changes to KE and then to heat in both the water and the rock.It is not necessary to calculate the KE so go straight to your equation which is the correct one.Make sure you plug in the right values for m and c.

Thanks for agreeing with me. Could you help me out now with making my physics teacher agree with me. He says that you add the energy of the rock with the heat from the rock to equal the heat of the water. mgh+mcT(rock)=mcT(water). I think it is wrong but I have no clue how to explain it. Do you know how.

The impression gained from your question was that the rock and water were both at the same temperature at the start. Let us assume they are not.
If the rock were colder then it would gain some of its heat energy from the heat energy of the water and if the water were colder it would gain some of its heat energy from the heat energy rock.If they were at the same temperature, which is what I assume from your question,then both would gain heat energy from the PE only and both of them would heat up.

## 1. How fast will the rock be traveling when it hits the bottom of the pail?

The rock will be traveling at a speed of approximately 19.8 meters per second when it hits the bottom of the pail.

## 2. What is the potential energy of the rock at the top of the 20 meter height?

The potential energy of the rock at the top of the 20 meter height is approximately 98 joules.

## 3. How much kinetic energy will the rock have when it hits the bottom of the pail?

The rock will have approximately 98 joules of kinetic energy when it hits the bottom of the pail.

## 4. Will the mass of the rock affect its acceleration?

According to the formula F=ma, where F is the force, m is the mass, and a is the acceleration, the mass of the rock will not affect its acceleration as gravity will provide the same acceleration for all objects regardless of their mass.

## 5. How long will it take for the rock to fall to the bottom of the pail?

Assuming no air resistance, it will take approximately 1.43 seconds for the rock to fall to the bottom of the pail.

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