The normal force on an incline is given by which expression?

The normal force on an incline is given by which expression?

• A. F_N = m g
• B. F_N = m g sin theta
• C. F_N = m g tan theta
• D. F_N = m g cos theta

Answer: (D)

On an incline, gravity can be separated into two components: one perpendicular to the surface and one parallel to it. The normal force is the contact force that balances the perpendicular component of gravity when there’s no motion into or away from the surface. That perpendicular component is m g cos theta, where theta is the angle between the surface and the horizontal. Therefore, the normal force is F_N = m g cos theta. This aligns with intuition: when the plane is flat (theta = 0), the normal equals the full weight mg; as the plane gets steeper, the perpendicular component—and thus the normal force—decreases. The component of gravity along the plane is m g sin theta, which drives sliding, not the normal force.

On an incline, gravity can be separated into two components: one perpendicular to the surface and one parallel to it. The normal force is the contact force that balances the perpendicular component of gravity when there’s no motion into or away from the surface. That perpendicular component is m g cos theta, where theta is the angle between the surface and the horizontal. Therefore, the normal force is F_N = m g cos theta. This aligns with intuition: when the plane is flat (theta = 0), the normal equals the full weight mg; as the plane gets steeper, the perpendicular component—and thus the normal force—decreases. The component of gravity along the plane is m g sin theta, which drives sliding, not the normal force.