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.
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, m v = m v -----1-1- (1)22 Where, m - m1s of first puck v1- velocity of first puck m2 mass of second puck v - velocity of second puck 2 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. Step 2 a) If the mass of one of the pucks is doubled, say m = 2m, then the velocity also will change 2 and we can use the same equation (1) for calculating the new velocity. It is, mv = 2mv 1 2 We know that the velocity of single puck is ‘v’. Therefore, v = v 1 That is, m v = 2mv 2 ‘m’ on both sides will get cancelled each other. Therefore, v = 2v 2 Or, v2= v/2 In other words, the velocity will get halved if the mass of one of the pucks is doubled.