Solution Found!
Answer: When two identical air pucks with repelling
Chapter 5, Problem 7P(choose chapter or problem)
Problem 7P
When two identical air pucks with repelling magnets are held together on an air table and released, they end up moving in opposite directions at the same speed, v. Assume the mass of one of the pucks is doubled and the procedure is repeated.
a. From Newton’s third law, derive an equation that shows how the final speed of the double-mass puck compares with the speed of the single puck.
b. Calculate the speed of the double-mass puck if the single puck moves away at 0.4 m/s.
Questions & Answers
QUESTION:
Problem 7P
When two identical air pucks with repelling magnets are held together on an air table and released, they end up moving in opposite directions at the same speed, v. Assume the mass of one of the pucks is doubled and the procedure is repeated.
a. From Newton’s third law, derive an equation that shows how the final speed of the double-mass puck compares with the speed of the single puck.
b. Calculate the speed of the double-mass puck if the single puck moves away at 0.4 m/s.
ANSWER:
Solution 7P
Introduction
According to Newton’s third law of motion, for every action, there will be an equal and opposite reaction. So, we can use this law here to proceed with this problem.
Step 1
According to the third law of motion, the momentum is conserved here.
Provided, both of these identical pucks will move with same speed ‘v’ to opposite directions if it is released once.
So, according to the law of conservation of momentum, m1v1 = m2v2 ----------- (1)
Where, m1- mass of first puck
v1 - velocity of first puck
m2- mass of second puck
v2 - velocity of second puck
Provided the pucks are identical and it moves with same speed,’v’ to opposite directions once it is released.
Consider the mass of the pucks initially as ‘m’ since both are identical. Then,
mv = mv and the law of conservation of momentum is valid here.