Find Thermal Energy & Initial Speed of Skidding 1200kg Car

[bigmac]

Homework Statement

A 1200kg car skids with uk = 0.45. If it skids 45.2m, find the thermal energy and the initial speed.

m = 1200 kg
Vi = ?
Vf = 0 m/s (i think..because it wants to stop)
uk = 0.45 (coefficient of friction)
delta d = 45.2m

Homework Equations

Well for Frictional force we use Ff = uk x Fn (0.45x11760) = 5292N

The Attempt at a Solution

So I found the Fn which is 1200 x 9.8 = 11760 N

Then I found Ff which is 0.45 x 11760 = 5292 N

Then I found the work done (I don't know why thermal energy is the work can someone explain this please)

W = F x d = 5292 x 45.2 = 239198.4 J

But my textbook's answer key has a different answer for the thermal energy, it says it should be 5.3 kJ and 72km/h for the speed. How do we find the speed?

 

[tiny-tim]

I don't know why thermal energy is the work can someone explain this please

Hi bigmac!

work done = loss in energy (the work-energy equation), and nearly all the energy lost is thermal.

So they're different things, but they're equal in value.

And once you have the thermal energy, you can equate it to ∆(KE)

… W = F x d = 5292 x 45.2 = 239198.4 J

But my textbook's answer key has a different answer for the thermal energy, it says it should be 5.3 kJ and 72km/h for the speed. How do we find the speed?

Are you sure it doesn't say 5.3 kN ?

Using your figure for W, I do get 72km/h for the speed.

 

[kerimek]

First of all, great job on finding the frictional force and work done! To find the thermal energy, we need to understand that the work done by friction is converted into heat, which is a form of thermal energy. This is because the car's brakes are rubbing against the road surface, causing friction and therefore heat. So, the work done you calculated is actually the thermal energy produced during the skidding.

To find the initial speed of the car, we can use the equation for kinetic energy: KE = 1/2mv^2. We know the mass of the car (1200kg) and we can assume that the final kinetic energy is 0 (since the car comes to a stop). So, we have:
KE = 1/2(1200)(Vi)^2
0 = 1/2(1200)(Vi)^2
0 = 600(Vi)^2
Vi = √(0/600) = 0 m/s

This means that the initial speed of the car was 0 m/s, which makes sense since it comes to a stop during the skidding. However, the answer key states the initial speed as 72 km/h. This could be a mistake or there may be additional information missing from the problem statement. Without knowing the exact context, it is difficult to determine the correct answer.

In conclusion, you have correctly calculated the thermal energy and the initial speed of the car is 0 m/s. If there is additional information or context that can help clarify the discrepancy in the answer key, please provide it so we can further assist you.