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.%0D%0A%0D%0AAt minimum, how much force will the second mover need to apply to help push the couch up the ramp?%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A30 N%0D%0A30 N%0D%0A%0D%0A80 N%0D%0A80 N%0D%0A%0D%0A31 N%0D%0A31 N%0D%0A%0D%0A110 N

Answer 1

To determine the minimum force that the second mover needs to apply in order to help push the couch up the ramp, let's analyze the forces involved.

1. Force applied by the first mover (F1): 80 N to the right.
2. Frictional force (F_friction): 110 N to the left.

The total force being exerted to the right (toward pushing the couch up the ramp) is the force from the first mover, while the total force resisting that movement (due to friction) is the frictional force.

To find the total force required to overcome the friction and push the couch up, we sum the frictional force and the force the first mover is applying.

The total leftward (friction) force that needs to be overcome is 110 N. The first mover is applying 80 N to the right.

Let \( F_2 \) be the force that the second mover applies. The equation considering all the forces in the horizontal direction is:

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

Substituting the known values:

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

Now, solving for \( F_2 \):

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

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

The correct response is 30 N.