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.
- Force applied by the first mover: 80 N to the right (up the ramp).
- 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.
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