A push F is directed at angle α above the horizontal. Which component of F is responsible for horizontal acceleration?

A push F is directed at angle α above the horizontal. Which component of F is responsible for horizontal acceleration?

• A. The horizontal component reduces the normal force.
• B. The vertical component increases friction.
• C. The vertical component F sin α reduces the normal force.
• D. The horizontal component does not affect horizontal motion.

Answer: (C)

When a push is angled above the horizontal, it has a horizontal part that tries to move the object along the surface and a vertical part that presses down or lifts up. The key is how friction depends on the normal force. The vertical component of the push reduces the normal force on the surface (the normal force becomes N = mg − F sin α for an upward component). With a smaller normal force, friction μN becomes smaller, so the opposing friction force decreases. That means the horizontal push can more effectively accelerate the object because there’s less friction resisting it. So the vertical component’s effect on the normal force—and thus on friction—makes horizontal acceleration possible. The horizontal component does contribute to pushing along the surface, but the reason you get horizontal acceleration in this situation is primarily the vertical component’s reduction of friction through a smaller normal force.

When a push is angled above the horizontal, it has a horizontal part that tries to move the object along the surface and a vertical part that presses down or lifts up. The key is how friction depends on the normal force. The vertical component of the push reduces the normal force on the surface (the normal force becomes N = mg − F sin α for an upward component). With a smaller normal force, friction μN becomes smaller, so the opposing friction force decreases. That means the horizontal push can more effectively accelerate the object because there’s less friction resisting it. So the vertical component’s effect on the normal force—and thus on friction—makes horizontal acceleration possible. The horizontal component does contribute to pushing along the surface, but the reason you get horizontal acceleration in this situation is primarily the vertical component’s reduction of friction through a smaller normal force.