Sled Pull with Changing Force
Two students pull a 40 kg sled across level snow. With a steady pull of 60 N, the sled moves at a constant 1.5 m/s. The force of kinetic friction is 60 N. The students then pull with 80 N in the same direction while the sled is already moving; friction remains 60 N for the next several seconds. A classmate says, 'The sled was already moving at constant speed, so adding force will not change anything until the pulling force is greater than the sled's weight.' Another says, 'At constant speed there is no force at all, so the rope is not doing anything.' The teacher asks the group to use net force and Newton's laws to predict the sled's motion during the 80 N pull and after the students stop pulling.
1. Calculate the net force on the sled during the 80 N pull and its acceleration. Include direction.
Read the worked answer
The horizontal forces are the pull forward and friction backward. Take the direction of motion as positive.
Net force = 80 N - 60 N = 20 N forward.
Use Newton's second law, Fnet = ma: a = Fnet / m = 20 N / 40 kg = 0.50 m/s^2.
The acceleration is 0.50 m/s^2 in the direction of motion. Since the sled is already moving forward, it speeds up at that rate. The vertical forces, weight and normal force, are balanced and do not affect the horizontal acceleration.
2. Explain why the sled can move at constant velocity with a 60 N pull, and critique both student statements.
Read the worked answer
At constant velocity, acceleration is zero, so the net force must be zero. The 60 N pull forward is exactly balanced by 60 N of kinetic friction backward. The sled keeps moving because of inertia, not because a net force is needed to maintain motion.
The first student is wrong: the sled's weight is vertical and is balanced by the normal force. Weight does not need to be exceeded for horizontal motion to change; the horizontal net force controls horizontal acceleration. The second student is also wrong: forces are present even when they balance. The rope pulls forward and friction pulls backward; they simply cancel. Balanced forces do not mean no forces exist.
3. Predict the sled's motion after the students stop pulling. Explain using Newton's laws.
Read the worked answer
After the students release the rope, the only horizontal force is kinetic friction, 60 N opposite the motion. The net force is therefore 60 N backward, so: a = 60 N / 40 kg = 1.5 m/s^2 backward.
The sled slows down at 1.5 m/s^2 and eventually stops. This is consistent with Newton's first law because the net force is no longer zero, so the velocity changes. If friction were zero, the sled would continue at constant velocity after release. The stopping is caused by the unbalanced friction force, not by a lack of force keeping it moving.