A red car with a 70kW engine and a mass of 1335kg accelerates at full power for 2s from rest along a level stretch of road heading east before going down a 3m high hill. The driver puts the car in neutral to accelerate as they coast down the hill. Some distance beyond the hill on another level stretch of road is an intersection. A blue car of mass 1800kg drives south at 60km/h into this intersection in front of the red car. The driver of the red car sees this and hits the brakes but is unable to stop in time and collides in elastically with the blue car. The tangled wreck of the cars slides off across the intersection with a velocity of 20km/h 30° south of east. During braking the four 8kg brake drums (drums of mainly iron of 22.86cm in diameter) of the red car heat up. If the specific heat of iron is 448J/kg°C and the linear expansion coefficient of iron is 11x10-6°C, by how much does the diameter of the brake drum change? Assume there is no energy loss or friction other than within the brakes and that the car maintains a constant velocity after the hill and before applying the brakes.
helppppppppp!!!!!!!!
The collision cannot be elastic if they combine in a "tangled wreck".
Perhaps they meant inelastic.
There is no reason to believe that the kinetic energy loss would end up on the brake drums.
This problem makes no sense at all.
@drwls:
The "elastic" part was a typo because it says "in elastically" above; an unnecessary space was put in.
With regards to the KE loss not necessarily ending up on the brake drums, I'd say that you are correct, but this looks to be an idealised problem with certain assumptions to stretch the student's physics understanding, rather than a realistic one.
Considering all this, does it make more sense now?
To determine the change in diameter of the brake drum, we need to consider the change in temperature and the linear expansion coefficient of iron.
First, we need to calculate the change in temperature of the brake drum. We know that the specific heat of iron is 448 J/kg°C. However, we are not given the mass or the change in temperature of the brake drum, so we cannot directly calculate the change in temperature.
Instead, we need to use the information given in the problem to find the necessary values. The fact that the brake drums heat up while braking suggests that the energy from the braking is transferred to the brake drums, causing them to increase in temperature.
Once we have the change in temperature, we can use the linear expansion coefficient of iron to calculate the change in diameter.
Unfortunately, the given problem does not provide enough information to calculate the change in diameter of the brake drum. We would need additional data, such as the initial and final temperatures of the brake drums or the energy transferred to the brake drums during braking.
Therefore, without the required information, it is not possible to determine the change in diameter of the brake drum in this scenario.