How much force is required to keep a 780 N box moving at constant velocity across thefloor if the friction force between the box and the floor is 160 N?

1. Break Down the Problem

To determine the force required to keep the box moving at a constant velocity, we need to consider the forces acting on it. In this scenario, the box has a weight of 780 N and experiences a frictional force of 160 N opposing its motion.

2. Relevant Concepts

According to Newton's first law, an object that is in motion will remain in motion at a constant velocity unless acted upon by a net external force. To maintain a constant velocity, the applied force must equal the frictional force opposing the motion.

3. Analysis and Detail

Let:

• $F_{\text{applied}}$ = force applied to keep the box moving
• $F_{\text{friction}}$ = frictional force

Because the box is moving at a constant velocity, we can set the magnitudes of the applied force and the frictional force as equal:

$F_{\text{applied}} = F_{\text{friction}}$

Given:

• $F_{\text{friction}} = 160 \, \text{N}$

Thus,

$F_{\text{applied}} = 160 \, \text{N}$

4. Verify and Summarize

Since the applied force must equal the frictional force to keep the box moving at constant velocity, we find that the force required is indeed equal to the given friction force.

Final Answer

The force required to keep the 780 N box moving at constant velocity across the floor is 160 N.