Q3.4 Misapplying the Third Law (T,K)
Santa Claus asks Rudolph to pull his sleigh. “It is pointless even to try,” replies Rudolph. “By Newton’s 3rd Law, if I exert a force on the sleigh, the sleigh will exert an equal and opposite force on me. The two forces will cancel, and we will get nowhere.”
Put Rudolph’s physics right.
Hint
Reveal

Hint
What is the key thing to remember about the two forces that are related by the 3rd Law? (Key Point 2.3).Solution
Reveal

Solution
Rudolph is half-right. His first assertion is correct: whatever force he exerts on the sleigh, the sleigh will exert exactly the same magnitude of force on him. But the second assertion is wrong: the forces cannot ‘cancel’ because they act on different bodies (as is invariably the case for the two forces that make up an action-reaction pair) –one acts on the sleigh (and is relevant to whether the sleigh moves) the other acts on Rudolph (and is relevant to whether he moves).
To determine whether there is motion or not we must carefully identify a system and think about all of the forces that act on it in a horizontal direction.
If we choose Rudolph as the ‘system’ the forces involved are FRS (the force that the sleigh exerts on Rudolph) and FRG, the force that the ground exerts on Rudolph (in the horizontal direction). The first force acts to the left (holding him back) the second acts to the right, pulling him forward. He will move forward if he can make the latter bigger than the former. How does he do this? Simply by pushing backwards on the ground hard enough: by the third law the force FRG that the ground exerts on him will always match (in magnitude) the force FGR he exerts on the ground. Along with Rudolph, we walk by courtesy of the 3rd law.