Fred and Joe are moving identical boxes across a floor where there is friction present. Fred pushes his box with a force that is directed 20 degrees below the horizontal, while Joe pulls his box using a rope that is angled 20 degrees above horizontal. Who must use the greater force and why.
To determine who must use the greater force, we need to analyze the forces acting on each box and consider the effects of the angles.
First, let's break down the forces acting on Fred's box:
- The applied force (Fred pushing the box) is at an angle of 20 degrees below the horizontal.
- The force of friction between the box and the floor acts in the opposite direction of motion, which is horizontal. Therefore, it acts against the applied force.
Next, let's consider the forces acting on Joe's box:
- The applied force (Joe pulling the box) is at an angle of 20 degrees above the horizontal.
- The force of friction between the box and the floor acts in the opposite direction of motion, which is horizontal. Therefore, it also acts against the applied force.
When the applied force is inclined, only the horizontal component of the force contributes to overcoming the friction. The vertical component of the force does not affect the motion because the friction force acts perpendicular to it.
Since both boxes are identical and experiencing the same friction force, the boxes require an equal force to overcome the friction. However, the angle of application does affect the magnitude of the force required.
The force required to overcome friction is directly proportional to the horizontal component of the applied force. As the angle of the applied force increases, the horizontal component decreases. This means that Fred, who pushes the box with a force at an angle below horizontal, will require a greater force to overcome the friction compared to Joe, who pulls the box with a force at an angle above horizontal.
Therefore, Fred must use the greater force compared to Joe because the angle at which he applies the force reduces its effectiveness in overcoming the friction.