Newton's Third Law: Acceleration of box and worker

In summary: If the push was in the opposite direction then the box would not move and if the push was exactly equal to the weight then the box and worker would both have the same acceleration.
  • #1
mitchy16
23
2

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.
 
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  • #2
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.
 
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  • #3
mitchy16 said:
why is it not A
Because forces and accelerations are vectors - direction matters.
 
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Related to Newton's Third Law: Acceleration of box and worker

What is Newton's Third Law?

Newton's Third Law states that for every action, there is an equal and opposite reaction.

How does Newton's Third Law apply to the acceleration of a box and worker?

According to Newton's Third Law, when the worker pushes against the box, the box exerts an equal and opposite force on the worker. This causes the worker to accelerate in the opposite direction of the box, as the forces are equal and opposite.

Can you provide an example of Newton's Third Law in action?

One example of Newton's Third Law in action is when a person jumps off a diving board. As they push down on the board, the board exerts an equal and opposite force on the person, propelling them upwards.

Does Newton's Third Law only apply to objects in motion?

No, Newton's Third Law applies to all objects, whether they are in motion or at rest. The law describes the relationship between forces and does not depend on an object's state of motion.

How does Newton's Third Law relate to force pairs?

Newton's Third Law describes force pairs, which are two forces that are equal in magnitude and opposite in direction. These forces always act on different objects and are a result of the interaction between the objects.

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