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.

Question

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

(1 point)
Responses

110 N
110 N

30 N
30 N

31 N
31 N

80 N

Answer 1

To determine the minimum amount of 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. The first mover is applying a force of 80 N to the right.
2. The force of friction opposing the motion is 110 N to the left.

To move the couch up the ramp, the total force applied (the force from both movers) must exceed the frictional force.

Let's denote \( F_2 \) as the force that the second mover needs to apply. The total force acting to the right would then be \( 80 \text{ N} + F_2 \).

For the couch to move up the ramp, we need:

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

Now, we can rearrange this to find \( F_2 \):

\[ F_2 > 110 \text{ N} - 80 \text{ N} \] \[ F_2 > 30 \text{ N} \]

Since we are looking for the minimum amount of force, the second mover must apply at least 31 N to ensure that the total force exceeds the friction force.

Therefore, the correct response is:

31 N.