# Newton's Third Law: Acceleration of box and worker

## Homework Statement

On a horizontal frictionless floor, a worker of weight 0.900 kN pushes horizontally with a force of 0.200 kN on a box weighing 1.80 kN. As a result of this push, which statement could be true?
A ) The box will not move because the push is less than its weight.
B ) The worker will accelerate at 2.17 m/s2 and the box will accelerate at 1.08 m/s2, but in opposite directions.
C ) The worker and box will both have an acceleration of 2.17 m/s2, but in opposite directions.
D ) The worker and box will both have an acceleration of 1.08 m/s2, but in opposite directions.
E ) The worker will accelerate at 1.08 m/s2 and the box will accelerate at 2.17 m/s2, but in opposite directions.

## Homework Equations

F=ma
FA on B = -FB on A

## The Attempt at a Solution

(converted all kN to N first)
Solving for mass:
WORKER:
w = mg
900N = m(9.8m/s2)
91.836 kg = m
BOX:
w = mg
1800N = m(9.8m/s2)
183.67 = m

Solving for acceleration:
WORKER:
F=ma
200 = (91.836)(a)
2.17 = a
BOX:
F=ma
-200=(183.67)(a)
-1.08 = a

I got the answer B, which is correct but why is it correct? I did all the work and got it, but why is it not A? Is it because Newton's third law? Sorry, just don't understand why this is correct.

Nugatory
Mentor
There are three different forces acting on the box. What are they and what do they add up to? If the sum is non-zero then the box will accelerate.

There are three different forces acting on the worker. What are they and what do they add up to? If the sum is non-zero then the worker will accelerate.

Yes, you will need Newton's third law to identify some of these forces.

• mitchy16
haruspex
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