how do you figure out the speed of an object after an elastic collision?

Question

A 0.400 kg toy truck moving at an initial speed of 0.100 m/s collides head-on with a 0.300 kg toy car at rest. The collision is elastic. Find their final speeds and directions.
a. v1 = 0.100 m/s v2 = 0.0 m/s
b. v1 = 0.0 m/s v2 = 0.100 m/s
c. v1 = 143 m/s v2 = 114 m/s
d. v1 = 0.0143 m/s v2 = 0.114 m/s

Answer 1

In any interaction momentum (m x v) is conserved.

In any elastic collision, kinetic energy (m x v x v / 2) is conserved.

Answer d is the only one to conserve momentum (they sum to 0.04 kg-meters/sec).

Answer d is also the only to conserve kinetic energy, (they sum to 0.002 kg m m /sec/sec).

Use either or both if you have to show your work. Use both to solve it without having multiple choice answers to choose from.

If you don't have to show any work, use Harry's logical arguments.

Answer 2

Common sense helps with this multiple choice question, but I bet you want a more general method. The system of equations given by the conservations of momentum and energy are often difficult to solve.



Here is the concise solution for head-on collisions. First, calculate the reduced mass,

M = m1 m2 / (m1 + m2) .... same as .... 1/M = 1/m1 + 1/m2.

The momentum transfer equals

ΔP = 2 M v0

where v0 is the original relative speed of the projectile.



Once we have this it is easy. In your case, m1 = 0.400 kg, m2 = 0.300 kg, so M = 0.12 / 0.7 = 0.1714 kg. The momentum transfer is equal to

ΔP = 2 * 0.1714 * 0.100 = -0.03428 kg m/s

The velocity loss by the truck is
Δv1 = -ΔP / m1 = -0.03428 / 0.400 = -0.0857
and its final speed
v1 = 0.100 + -0.0857 = 0.0143 m/s

The velocity gain by the car is
Δv2 = ΔP / m2 = -0.03428 / 0.300 = 0.0114 m/s
and its final speed is
v2 = 0.0114 m/s

Answer 3

By common sense mate, the first and second solutions are false, because for either of the balls to come to a stop they must be of equal size. The 3rd is completely wrong since a relatively large amount of energy has been added to the system. Therefore the fourth (d) is correct...Just look at the figures in (c)!!

Answer 4

for elastic collision momentum is conserved
m1*v1 = m2*v2
so .4*.1 = .4v1 + .3v2
also KER is conserved
1/2*.4*.1^2 = 1/2*.4*v1^2 + 1/2*.3*v2^2
solving this
ans is d

Answer 5

d