A horse pulls a sled along a level, snow-covered road, causing the sled to accelerate, as shown in Figure 5.18a. Newton’s third law states that the sled exerts a force of equal magnitude and opposite direction on the horse. In view of this, how can the sled accelerate—don’t the forces cancel?

Question

A horse pulls a sled along a level, snow-covered road, causing the sled to accelerate, as shown in Figure 5.18a. Newton’s third law states that the sled exerts a force of equal magnitude and opposite direction on the horse. In view of this, how can the sled accelerate—don’t the forces cancel? Under what condition does the system (horse plus sled) move with constant velocity?

Accepted Answer

Remember that the forces described in Newton’s third law act on different objects—the horse exerts a force on the sled, and the sled exerts an equal-magnitude and oppositely directed force on the horse. Because we are interested only in the motion of the sled, we do not consider the forces it exerts on the horse. When determining the motion of an object, you must add only the forces on that object.
(This is the principle behind drawing a free-body diagram.) The horizontal forces exerted on the sled are the forward force T exerted by the horse and the backward force of friction [latex] f _{ ext {sled }} [/latex] between sled and snow (see Fig. 5.18b). When the forward force on the sled exceeds the backward force, the sled accelerates to the right.
The horizontal forces exerted on the horse are the forward force [latex] f _{ ext {horse }} [/latex] exerted by the Earth and the backward tension force T exerted by the sled (Fig. 5.18c). The resultant of these two forces causes the horse to accelerate.
The force that accelerates the system (horse plus sled) is the net force [latex] f _{ ext {horse }}- f _{ ext {sled }} ext {. When } f _{ ext {horse }} ext { balances } f _{ ext {sled }} [/latex], the system moves with constant velocity.

Question 5.11: A horse pulls a sled along a level, snow-covered road, causi...

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