Question

(a) An object that has a small mass and an object that has a large mass have the same momentum. Which object has the largest kinetic energy? (b) An object that has a small mass and an object that has a large mass have the same kinetic energy. Which mass has the largest momentum?

Answer 1

Answer:

A) The smaller object; B) The larger object

Explanation:

A) Lets say the small object is 2 kg and the large one is 6 kg. Lets say they also have 30 kg*m/s of momentum each. The small object would have 15 m/s velocity and the large would have 5 m/s.

Now for kinetic energy(.5*m*v²), the small object is .5*2*15², which is 225 J

The large object is .5*6*5², which is 75 J, so the smaller object has more Kinetic energy. Since velocity is squared, it is more important than how large mass is.

B) Same masses as part A. Lets say the kinetic energy is 45 J for both of them. For the small object, 45=.5*2*v²

.5*2 is 1, so 45/1 is 45. Take the square root and we get v= 6.71 m/s

For the large object, 45=.5*6*v²

.5*6 is 3, so 45/3 is 15. Take the square root and we get v=3.87 m/s

Now we plug the velocities into p=mv

For the small object, p=2*6.71, which gives us p=13.42 kg*m/s

For the large object, p=6*3.87, which gives us p=23.22 kg*m/s

The larger object has the larger momentum.

Hope this helps