A mass, m, is pulled along a horizontal surface by force F,...

A mass, $m,$ is pulled along a horizontal surface by force $F,$ as shown above. If the resulting motion is constant velocity, then the frictional force is equal to
(A) zero
(B) $\mu m g$
(C) $m g \cos \theta$
(D) $F \cos \theta$
(E) $F \sin \theta$

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Key Concepts

Newton's First Law

This law, also known as the law of inertia, states that an object will maintain its state of rest or uniform motion in a straight line unless acted upon by a net external force. In the context of constant velocity, it implies that the sum of all forces acting on the object is zero, which means the frictional force must exactly balance the applied force's horizontal component.

Force Decomposition

When a force is applied at an angle, it is resolved into horizontal and vertical components using trigonometric functions. The horizontal component (F cos ?) is responsible for moving the object along the surface, while the vertical component (F sin ?) affects the normal force. This resolution is key to analyzing forces in problems involving inclined or angled pulls.

Frictional Force

Friction is a resistive force that opposes the motion of an object sliding over a surface. In a situation where the object moves at constant velocity, the frictional force must balance the net applied force in the horizontal direction. This balance ensures that there is no net acceleration, thereby satisfying the condition for constant velocity.

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