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Dale and Alex push on opposite sides of a couch. Dale pushes to the left with a force of 250 N, while Alex pushes to the right with a force of 130 N. If the couch has a mass of 32 kg, what is the acceleration of the couch?

Verified Answer :

charleszuker

F=ma
a=F/m

F=+250N + (-130N)=120N LEFT
('m summing my forces because they are moving about the same axis, and the negative/positive accounts for the arbitrary directions I assign)
m=32kg

F=120N/32kg=3.75m/s^2 to the LEFT

3.75m/s^2 to the LEFT

boffeemadrid

The acceleration of the couch is required.

The acceleration of the couch is \(3.75\ \text{m/s}^2\) towards the left.

Let the direction towards the right be positive and left be negative.

\(F_1=-250\ \text{N}\)

\(F_2=130\ \text{N}\)

Net force

\(F=F_1+F_2\\\Rightarrow F=-250+130\\\Rightarrow F=-120\ \text{N}\)

m = Mass of couch = 32 kg

Force is given by

\(F=ma\\\Rightarrow a=\dfrac{F}{m}\\\Rightarrow a=\dfrac{-120}{32}\\\Rightarrow a=-3.75\ \text{m/s}^2\)

The acceleration of the couch is \(3.75\ \text{m/s}^2\) towards the left.

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