Physics Foundation q 10

Two people are pushing on a box of mass 80 kg. One person applies a force of 100 N, and
the other applies a force of 200 N in the same direction. A frictional force of magnitude 80
N acts in the opposite direction. What is the acceleration of the box?
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As with any dynamics question, we'll use a three-step method:
1.  Free-body diagram
2.  Newton's second law
3.  Solve for what we need

The free body diagram here should have our box with all the forces labeled.  For consistency's sake, I'll call right positive, and up positive.  The forces we have are:
-Gravity, which is equal to mg = 80 kg(10 m/s²) = 80 N [downwards]
-Two applied forces, both acting towards the right, equal to 100 N and 200 N.
-Friction, equal to 80 N.  Since friction will ALWAYS oppose motion, we should know that it would be oriented towards the left, even if they didn’t tell us that in the question stem.
-Normal force, equal to 80 N.  The normal will be perpendicular to the surface between the objects, and here, that means it's oriented upwards.

Our second step will be Newton's second law, F = ma.
There's no acceleration in the up/down direction, so we'll ignore Newton's second law in that dimension.  However, there is acceleration left/right.  So let's set up Newton's second law:
Fnet = ma.
If right is positive, then our forces that direction are +100N and +200 N.  Friction is to the left, so it's -80N.
Fnet is then 100N + 200N - 80N = 220N.  Our mass is 80 kg, so we can rewrite Newton's second law as:
220N = 80kg (a).  Solving for a (our third step), we get 220N/80kg = 2.75 m/s²
Hope this helps!