Honors Physics Momentum Problem

[fantolay]

Homework Statement

A .45kg ice puck, moving east with a speed of 3 m/s has a head-on collision with a .9 kg puck initially at rest. Assuming a perfectly elastic collision, what will be the speed and direction of each object after the collision?

M1 = .45kg
M2 = .9kg
V1 = 3m/s
V2 = 0m/s

Perfectly elastic collision means Kinetic Energy and Momentum are conserved.

Homework Equations

KE = 1.2 * m * v²
P = m * v

The Attempt at a Solution

KE_I = KE_F (Initial KE = Final KE)
1/2 * m₁ * v₁² + 1/2 * m₂ * v₂² = 1/2 * m₁ * (v₁')² + 1/2 * m₂ * (v₂')²

and

P_I=P_F
m₁ * v₁ + m₂ * v₂ = m₁ * v₁' + m₂ * v₂'

I don't really know where to go from here or if this is the right start...

Thanks in advance

 

[Hunterbender]

You do have the right start. The rest is just really ugly algebra and moving things around.

Also, there is no such thing as kinetic energy conservation. Kinetic energy is not conserve, but energy is conserve. It just happens that there is no potential energy in your problem.

 

[thomate1]

for any help!

I would approach this problem by first identifying the given variables and their units, as well as the quantities that need to be solved for. In this case, we have the masses (m1 and m2) in kilograms and velocities (v1 and v2) in meters per second. We are asked to find the final velocities (v1' and v2') in the same units.

Next, I would use the given information to set up the equations for conservation of kinetic energy and momentum. These are fundamental principles in physics that state that these quantities are conserved in a closed system, such as in this collision. This means that the total kinetic energy and total momentum of the system before the collision (KEI and PI) must equal the total kinetic energy and total momentum after the collision (KEF and PF). These equations can be written as:

KEI = KEF (1/2 * m1 * v12 + 1/2 * m2 * v22 = 1/2 * m1 * (v1')2 + 1/2 * m2 * (v2')2)

and

PI=PF (m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2')

From here, we can substitute the given values for the masses and velocities and solve for the final velocities. For example, we can substitute m1 = 0.45kg, m2 = 0.9kg, v1 = 3m/s, and v2 = 0m/s into the equations to get:

KEI = KEF (1/2 * 0.45kg * (3m/s)2 + 1/2 * 0.9kg * (0m/s)2 = 1/2 * 0.45kg * (v1')2 + 1/2 * 0.9kg * (v2')2)

and

PI=PF (0.45kg * 3m/s + 0.9kg * 0m/s = 0.45kg * v1' + 0.9kg * v2')

Solving these equations simultaneously will give us the final velocities of the two objects after the collision. We can also use these equations to check if the collision is indeed perfectly elastic, as the kinetic energy and momentum should be conserved