Question

1. A sled of mass m is pushed for 5 seconds at a constant force. A sled of mass M (more) is also pushed for 5 seconds. THe force is the same in each case. WHat is the momentum of each sled? How do they compare? What is the energy of each sled? How do they compare?

2. The same question, except that each sled is pushed for 5 meters instead of 5 seconds.

Answer 1

(1)

accleration of mass m

a = F/m

so velocity

v = u + at

u = 0

v = 5F/m

so

momentum = m*v = 5F

now acceleration of mass M

A = F/M

velocity will be

V= U+At

U = 0

V = 5F/M

so momemtum = M*V = 5F

HENCE THE MOMEMTUM OF BOTH WILL BE SAME

now kinetic energy of mass m = 1/2 * m* v² = 1/2 * m * 25F² /m²

                                              = 25F² /m

kinetic energy of mass M = 1/2 * M * V² = 1/2 * M * 5F² /M²

                                      = 25F² / M

FROM THESE WE CONCLUDE THAT THE KINETIC ENERGY OF THE WO CASES IS NOT SAME

(2) now when the distance if 5m

velocity of mass m =

velocity of mass M =

so momemtum of mass m = m*v =

momemtum of mass M =

HENCE THE MOMEMTUM ARE NOT SAME

kinetic energy of mass m = 1/2 *m *v² = 1/2 * m * 10F/m

                                      = 5F

kinetic energy of mass M = 1/2 * M * V² = 1/2 *M * 10F/M

                                      = 5F

HENCE THE KINETIC ENERGY ARE NOW SAME FOR BOTH THE CASES