Question

Two movers are attempting to push a couch up a ramp. One mover applies a force of 80 N to the right, but the force of friction between the couch and the ramp is providing a force of 110 N in the opposite direction, and the couch slides down the ramp.

At minimum, how much force will the second mover need to apply to help push the couch up the ramp?

Answer 1

To determine the minimum force the second mover needs to apply to push the couch up the ramp, we can analyze the forces acting on the couch.

1. **Identify the forces:**
- The first mover applies a force of \( F_1 = 80 \, \text{N} \) to the right (up the ramp).
- The friction force acting against the motion is \( F_f = 110 \, \text{N} \) (down the ramp).
- Let the force applied by the second mover be \( F_2 \) (also acting up the ramp).

2. **Net force required to move up the ramp:**
For the couch to move up the ramp, the total force acting up the ramp must overcome the friction force. Therefore, we can set up the equation:

\[
F_1 + F_2 > F_f
\]

3. **Substituting the known values:**
Replacing \( F_1 \) and \( F_f \) gives:

\[
80 \, \text{N} + F_2 > 110 \, \text{N}
\]

4. **Rearranging the inequality:**
To find the minimum force \( F_2 \):

\[
F_2 > 110 \, \text{N} - 80 \, \text{N}
\]

\[
F_2 > 30 \, \text{N}
\]

5. **Final result:**
Therefore, at minimum, the second mover needs to apply a force greater than \( 30 \, \text{N} \) to help push the couch up the ramp.

Thus, the answer is that the second mover needs to apply **at least 31 N** (since the force must be greater than 30 N) to ensure the couch moves up the ramp.