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 s 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 find out how much force the second mover needs to apply to help push the couch up the ramp, we can analyze the forces acting on the couch.

1. **Force applied by the first mover**: 80 N to the right (up the ramp).
2. **Force of friction**: 110 N to the left (down the ramp).

To find the net force required to just overcome the force of friction (in order to move the couch up the ramp), we can set up an equation:

Let \( F_2 \) be the force applied by the second mover.

The net force \( F_{\text{net}} \) pushing the couch up the ramp needs to overcome the force of friction:

\[ F_{\text{net}} = F_1 + F_2 - F_{\text{friction}} = 0 \]

where:
- \( F_1 = 80 \, \text{N} \) (force applied by the first mover)
- \( F_{\text{friction}} = 110 \, \text{N} \) (force of friction)

Substituting into the equation, we can write:

\[ 80 \, \text{N} + F_2 - 110 \, \text{N} = 0 \]

To find \( F_2 \), we can rearrange the equation:

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

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

So, the second mover needs to apply a minimum force of **30 N** to help push the couch up the ramp.