Alfred, who weighs 40 kg, is sitting on a sled of mass 10 kg. What is the force the sled is acting upon Alfred

Question

Answer is 400 N downwards

Answer 1

Since Alfred is just sitting on the sled, he obviously is not accelerating either up or down, in fact, he is not even moving up or down.

Newton's 2nd Law says F = ma. Since a = 0 (he is not accelerating either up or down, then F (net force) must also be zero.

Alfred has 2 forces acting on him in the up-down direction and they must both counteract each other since the net force is zero. The 2 forces are: 1) the force of gravity, which is his mass times the acceleration due to gravity (about 10m/s²) so 40 kg times 10 m/s² = 400 N pointing downward toward the center of the earth. and 2) the force the sled is pushing back on him which we typically call the Normal Force. Again, since these 2 forces must be equal and opposite to counteract one another, that force is 400 N as well but is pointing up towards the sky so that it counteracts the force of gravity.

The mass of the sled doesn't matter in this discussion since we are only talking about Alfred.

Here is a free body diagram:

So the answer is not 400 N downwards, it is 400 N upwards. It is the force of gravity on Alfred that is downwards.