Why Is Lowering a Box Considered Negative Work While Gravity Does Positive?

[Lolagoeslala]

Homework Statement

How come A person picks a 1.00-kg box of macaroni from off the shelf and lowers it 0.77 m into a shopping cart. The work done on the macaroni by the person is negative work however when person picks up a 1.00-kg box of macaroni from off the shelf and lowers it 0.77 m into a shopping cart. The work done on the macaroni by Earth is positive?

 

[ap123]

Remember that the work done involves the dot product between 2 vectors.
Look at the angle between the force and displacement vectors for these 2 cases.

 

[CWatters]

A person picks a 1.00-kg box of macaroni from off the shelf and lowers it 0.77 m into a shopping cart. The work done on the macaroni by the person is negative work

The force the man applies to the box is upwards (eg +ve), the displacement is downwards (-ve) so force * displacement is -ve.

It might seem strange that the force is upwards but consider how it works in practice... Let's say he lowers it slowly... First he picks it up then he reduces the vertical force he applies to the box so that it is less than the force due to gravity -> the box accelerates downwards. Then the man has to apply an upward force greater than that due to gravity to slow it to a stop at the new height. So the whole time the force he applies is upwards (+ve) even if for part of the time it's less than the force of gravity.

Another way to look at it... If the man raised the box and put it onto the shelf it would be fairly clear that he had done positive work. The force is still upwards (+ve) and the distance is also (+ve). So if raising the box means he's done +ve worj then it seems reasonable that if he lowers the box he does negative work on it.

when person picks up a 1.00-kg box of macaroni from off the shelf and lowers it 0.77 m into a shopping cart. The work done on the macaroni by Earth is positive?

The force due to gravity is downwards (-ve) and the distance is downwards (-ve). So force * distance is positive.