The brakes in a car increase in temperature by ?T when

Problem 5CQ

The brakes in a car increase in temperature by  when bringing the car to rest from a speed v. How much greater would  be if the car initially had twice the speed? You may assume the car to stop sufficiently fast so that no heat transfers out of the brakes.

                                                              Step By Step Solution

Step 1 of 3

Applying on brakes means applying friction force on the car to force it to stop. This friction force is performing a negative work on the car. Heat and work are the two distinct methods of energy transfer. And in this case ,all the work done will be transferred to heat energy inside the breaks,

Now we are assuming that the car stops fast enough that no heat transfers out of the brakes. And we are supposing that the force of the car’s break is constant in the two cases. So that,the negative acceleration of the car is constant too.

                                                                                                                  (1)

                                                                                                                (2)

                                                                                                         (3)

                                                                                    from (1)(2)(3)

                                                                                           (4)