# Forces and Acceleration

## Homework Statement

A courier is delivering a 5 kg package to an office high
in a tall building.
The courier uses the elevator to reach the office. While
the elevator (containing the courier who is holding the
package) is accelerating upwards at 0.11 m s−2 what up-
wards force is the courier applying to the package?

## The Attempt at a Solution

Ok so i know that the weight force acting on the package is 50N and I know that this will cause a reaction force of 50N upward onto the package.
But im a little confused. Every force has an equal and opposite reaction force right? so the package pushes down on the arm by 50N's and the arm reacts causing an upward force of 50N on the package this is all I get!!

somone please help ive been confused for hours on understanding this i dont just want the answer a physicsbased explanation would help me alot

cheers

cepheid
Staff Emeritus
Science Advisor
Gold Member

## The Attempt at a Solution

Ok so i know that the weight force acting on the package is 50N and I know that this will cause a reaction force of 50N upward onto the package.
But im a little confused. Every force has an equal and opposite reaction force right? so the package pushes down on the arm by 50N's and the arm reacts causing an upward force of 50N on the package this is all I get!!

Yeah, that would definitely be true if the package were stationary. Its weight would be exactly balanced by the force acting upward on it, so that it would not accelerate. However, in this situation, the package is not stationary. It is accelerating upwards. Therefore, the upward force on it must be larger than its weight. Another way of saying this is that there is a net upward force on the package.

net force = upward force - weight (≠ 0)​

You can figure out what this net force must be from Newton's Second Law (the acceleration and mass of the package are both given).

By the way, it would help greatly for this problem if you drew a free body diagram for the package.

Cheers I get it now.
But im sorta confused now about this.
Every action force has an equal and opposite reaction force right?
But the reaction force never acts in the same body as the action.
In this case wasnt the weight force the action force? and the upward normal reaction the reaction force? so how do they cancle ?

rl.bhat
Homework Helper

The elevator along with man is accelerating upwards. Due to inertia, the package tries to retain it position.Thus it pushes the hand in the down ward direction with an acceleration g. The reaction to this force by the hand is in the upward direction. Thus the net acceleration of the package is ( g+a)

cepheid
Staff Emeritus
Science Advisor
Gold Member

In this case wasnt the weight force the action force? and the upward normal reaction the reaction force? so how do they cancle ?

Hey, I think maybe rl.bhat explained this too, but basically, the answer to your question is that, in this situation, the action force is NOT the weight. Newton's third law still applies. What this means is that if the courier's arm pushes upward on the package with a force larger than its weight, then the package also pushes back down on the courier with this larger force. Therefore, the action and reaction forces are still equal in magnitude, but they are both larger than 50 N, due to the upwards acceleration of the system. Likewise, you feel heavier in an elevator when it first starts moving upwards, because the floor is pushing upward on you with a force larger than it usually does (i.e. larger than your weight).