Question

The magnitude of the initial momentum of this system (consisting of the two blocks), pi , is equal to m1ui . find an expression for the magnitude of the final momentum, pf , of this system. note that since m1>m2 , both objects will move in the positive direction after the collision. express pf in terms of m1 , m2 , uf , and vf ?

a) pf = m1vf + m2vf
b) pf = m1uf + m2uf
c) pf = m1uf - m2uf
d) pf = m1vf - m2vf

Answer 1

The expression for the magnitude of the final momentum, pf, of a system after a collision, given that m1>m2 and both blocks move in the same direction, is pf = m1•vf + m2•vf.

Step-by-step explanation:

To find an expression for the magnitude of the final momentum, pf, of a system consisting of two blocks, we use the conservation of momentum principle, which states that the momentum before a collision is equal to the momentum after the collision, provided no external forces act on the system. Given that block 1 with mass m1 and initial velocity ui collides with block 2 with mass m2 which is initially at rest, and after the collision, block 1 moves with final velocity vf and block 2 moves with final velocity vf (since m1 > m2), the final momentum of the system can be expressed as:

pf = m1•vf + m2•vf,

where vf is the final velocity of both blocks, as they move in the same direction after the collision. This corresponds to option (a).