Bill stands up still on Earth's surface. He weighs 50 Newtons. What is the force that the Earth exerts on him?
A. Greater than 50 N B. Less than 50 N c. Equal to 50 N
I am stuck between B or C. Is the force equal to his force, or is it less? He is standing still.
If he is not accelerating, the net force on him is $0$. This includes the gravitational force from the earth and the pressure from the ground on the soles of his feet. However, the earth's surface is not an inertial frame, so he actually is accelerating. The net force of the earth on him is the centripetal force corresponding to the earth's rotation. At the equator the centripetal acceleration would be about $0.03392 \; m/s^2$, which is about $.00346$ of the acceleration of gravity. The force is about $0.00346 \times 50 = 0.173\; N$. So the answer is B.
Given that the man stands still, there is no acceleration. According to the Newton’s Law, the total force that the earth exerts on the man is,
$$F=ma=m\cdot 0=0$$
So, the answer is B. Actually, there are two forces exerting on the man, one being the downward gravitational force and the other the upward supporting force by the earth surface. However, they cancel out.
