# What is the heat capacity of the tires of the car?

• aps0324
In summary, the problem involves calculating the heat capacity of the brakes on a car rolling down a slope and stopping after 10m, with no drag forces or heat transfer. The equation Q = mc(Tf-Ti) is used, where Q is the input energy, m is the mass of the brakes, c is the specific heat capacity, Tf and Ti are the final and initial temperatures. The change in potential energy and kinetic energy of the car are used to calculate the total energy input into the brakes. The internal energy change is not taken into account for simplicity. The final answer is that the heat capacity of the brakes is 6.25 x 10^3 Joule/Kelvin.
aps0324
1. Assume that a car who has a mass of 1000kg (including driver) is initially rolling freely (without using the engine) down a 30° slope at a speed of 5m/s. The brakes are used causing the car to stop after 10 m.

Find the HEAT CAPACITY of the brakes if they rise in temperature by 10 K.

Drag forces are negligible, no heat transfer to or from the car occurs and the only change in U (internal energy) is due to heating of the brakes

2. I need to find Q

Q = mc(Tf-Ti)

Using conservation of energy

W + Q = ΔK.E + ΔP.E + ΔU

W = sin(30) * d

K.E = (1/2)mv2

The rest I do not know?!

3. The answer is C =6.25 x 103 but I do not know how this is obtained.

What confuses me is the part that says that ΔU is not zero and that there is no heat transfer to or from the car.

What is the correct method in order to obtain that answer?

Thank you

Q = mc(Tf-Ti) is specific heat capacity, since you are not told the mass of the brakes - all you can do is work out the temperature change for the input energy.

You have Q = C(Tf-Ti), you have T, you found Q from the loss in ke and pe of the car, just drop it into the equation to get C

What confuses me is the part that says that ΔU is not zero and that there is no heat transfer to or from the car.
Thats just to make the problem solvable - you don't have to calculate the cooling of the brakes

How do I find the change in potential energy though?

Wouldnt I also need to know work and internal energy in order to find Q?

I do not understand...could you be kind enough ( or anybody else) to explain more?

Draw a diagram, the car goes 10m along the hypotonuse of a triangle an angle of 30deg - so you can work out how far vertically this is. together with the mass this gives you change in PE.
You are given the initial speed and presumably it brakes to zero, so you have the change in KE.

Thats the total energy going into the brakes, the heat capacity is just how many Joule/kelvin they rise in temperature

## 1. What is heat capacity?

Heat capacity is a measure of the amount of heat required to raise the temperature of a substance by a certain amount. It is typically measured in units of energy per degree Celsius or Kelvin.

## 2. Why is heat capacity important for tires?

Heat capacity is important for tires because it helps determine how much heat the tires can absorb before reaching their maximum temperature. This is important for maintaining proper tire pressure and preventing blowouts.

## 3. How is heat capacity of tires measured?

The heat capacity of tires can be measured using a calorimeter, which is a device that measures the amount of heat absorbed by a substance as it changes temperature. The tires are typically heated or cooled to a specific temperature and then placed in the calorimeter to measure the amount of heat absorbed.

## 4. What factors affect the heat capacity of tires?

The heat capacity of tires can be affected by several factors including the type of material the tires are made of, the size and shape of the tires, and the air pressure inside the tires. The composition of the road surface and the speed at which the car is traveling can also affect the heat capacity of the tires.

## 5. Can the heat capacity of tires be changed?

The heat capacity of tires is a physical property of the material and cannot be changed. However, it can be influenced by external factors such as the air pressure and speed of the car, which can affect the amount of heat the tires can absorb before reaching their maximum temperature.

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