Two skaters stand on friction-less ice. Ricky is more massive than Lucy. Ricky pushes off from Lucy and they move away from each other. Which statement below is most correct?
HINT: The total momentum of the system is zero before they push off, so the total momentum after the push must also be zero. Compare the two masses and the first hint statement and think about what this does to the velocities.
A) Ricky and Lucy will have the same momentum and speed after they push off.
B) Ricky and Lucy will have the same momentum, but Ricky will have a larger speed.
C) Ricky and Lucy will have the same momentum, but Lucy will have a larger speed.
D) Ricky will have a higher speed and therefore a higher momentum than Lucy.
E) Lucy will have a higher speed and therefore a higher momentum than Ricky.
F) Ricky and Lucy will have the same speed, but since Ricky is more massive he will have more momentum.
Using momentum conservation
Pi = Pf
Pi = MR*UR + ML*UL
UR = initial velocity of Ricky
UL = initial velocity of Lucy
Since UR & UL = 0 m/sec
Pi = 0 kg-m/sec
So from momentum conservation
Pf = 0
MR*VR + ML*VL = 0
MR*VR = -ML*VL
(Above relation means momentum of Ricky and Lucy will be same)
VL/VR = -(MR/ML)
MR > ML
MR/ML > 1
from above relation
VL/VR > 1
VL > VR
So speed of Lucy will have a larger speed than Ricky
Correct option is C.
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