Posted by Meg on .
Consider two cars, a very large one like a Hummer (mass 5m) and a small one like a Mini Cooper (mass m), both starting at the same point race toward the edge of a cliff. Assume that each car is accelerated by a constant force (same size force on each car) to the edge of the cliff.
A. which car has the greater acceleration?
B. Which car takes longer to reach the edge?
C. Which car has the larger impulse imparted to it by the applied force?
D. Which car has the greater momentum at the edge ?
E. WHich car has the greater work done on it?
F. Which car has the greater kinetic energy at the edge of the cliff?
A. From F=ma i'd say it would be the hummer as its got greater mass, and as Force is constant
A) With F=ma you get m=F/a. If F is a constant then; when mass increases the acceleration decreases and vice-versa (it's reversely proportional). So the Mini Cooper with lower mass has a greater acceleration.
B) With the above conclusion it is sensible that the Hummer takes a longer time.
C) Well impulse is measured by F*t. As F is a constant the Hummer which consumes more time(low acceleration) has a larger impulse.
D) We know that the impulse equals to the change of momentum. So it's the Hummer that has the greater momentum.
E) Work is the Force into the displacement of the center of mass. Here the Force is a constant and the displacement is the same for both cars. So it's reasonable enough to say that the work done on each car is equal.
F) Considering the work done is same for both cars, you easily get the answer that the Kinetic energies of the two cars are equal.