Which expression represents the gravitational force on a block of mass m?

• A. F_g = m g
• B. F_g = m g sin theta
• C. F_g = F_N
• D. F_g = mu m g

Answer: (A)

Gravitational force, or weight, is the product of mass and the strength of gravity. Near Earth, its magnitude is F_g = m g and it points downward. This quantity depends only on how much matter you have and how strong gravity is, not on the orientation of a surface or any friction.

The other forms mix in aspects that are not the total weight: on an incline, the weight can be resolved into components, with along the slope equal to m g sin theta and perpendicular to the slope equal to m g cos theta (the latter is balanced by the normal force). Friction is proportional to the normal force, F_f = μ F_N = μ m g cos theta, not gravity itself. So F_g = m g is the correct expression for the gravitational force.