Momentum and Impulse. find final velocity

[maxjohnfresh]

Homework Statement

A 0.10-kg object moving initially with a velocity of 0.20 m/s eastward makes an elastic head-on collision with a 0.15-kg object initially at rest. What is the final velocity of the .10 kg object after the collision ?

Homework Equations

im not sure which equation to use :/

The Attempt at a Solution

i tried using m1v1+m2v2=(m1+m2) V
but it didnt come out right.

and i know the answer is -0.045 m/s

 

[rl.bhat]

Hi maxjohnfresh, welcome to PF.
i tried using m1v1+m2v2=(m1+m2) V
This formula is true if both objects move together after collision.
So use the formula
m1v1i+m2v2i=(m1v1f+m2v2f) .
Apply the conservation of energy and solve for v1f and v2f.

 

[kerimek]

eastward.


I would suggest using the equations for conservation of momentum and conservation of kinetic energy to solve this problem.

First, we can calculate the initial momentum of the system using the equation p = mv, where p is momentum, m is mass, and v is velocity. In this case, the initial momentum of the system is (0.10 kg)(0.20 m/s) = 0.02 kg*m/s.

Next, we can use the conservation of momentum equation, p1 + p2 = p1' + p2', where p1 and p2 are the initial momenta of the two objects, and p1' and p2' are the final momenta after the collision. Since p2 is initially at rest, its momentum is 0, so the equation becomes p1 = p1'.

Substituting in the values, we get 0.02 kg*m/s = (0.10 kg)v1'. Solving for v1', we get v1' = 0.02 kg*m/s / 0.10 kg = 0.2 m/s eastward.

Finally, we can use the conservation of kinetic energy equation, KE1 + KE2 = KE1' + KE2', where KE is kinetic energy. Since the collision is elastic, kinetic energy is conserved, so the equation becomes KE1 = KE1'. Substituting in the values, we get (1/2)(0.10 kg)(0.20 m/s)^2 = (1/2)(0.10 kg)(v1')^2. Solving for v1', we get v1' = 0.2 m/s.

Therefore, the final velocity of the 0.10 kg object after the collision is 0.2 m/s eastward. This is the same as the initial velocity, indicating that the collision was perfectly elastic and the object did not lose any kinetic energy.