A student pushes a heavy box that is already moving across a rough floor. If the force applied by the student is exactly equal to the frictional force opposing the motion, what will happen to the box?
The box will move at a constant speed
To solve this problem, we need to understand the dynamics of motion under the influence of forces, particularly when the net force is zero.
Explanation:
- When an object is moving across a surface, it is subjected to various forces, including the force exerted by the person and the frictional force from the surface.
- Frictional force is a resistive force that opposes the relative motion of two surfaces in contact. In this case, it's opposing the motion of the box.
- According to Newton's First Law of Motion, an object will continue in its state of rest or uniform motion unless acted upon by a net external force. This implies that if the forces acting on the object are balanced, the object will continue its motion with constant velocity.
When the force applied by the student is exactly equal to the frictional force, the forces cancel each other out, resulting in a net force of zero. Since the net force is zero, there is no change in the box's velocity.
Conclusion:
Thus, the box will continue to move at a constant speed.
Justification of Options:
- The box will move at a constant speed (Correct answer): With balanced forces (net force = 0), the box maintains its current speed.
- The box will gradually come to rest: This would occur if the frictional force were greater than the applied force, resulting in deceleration.
- The box will move at an increasing speed: This would happen if the applied force were greater than the frictional force, resulting in acceleration.
- The box will accelerate forward: Similar to moving at increasing speed, this requires a greater applied force than frictional resistance.
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