An elevator is used to either raise or lower sacks of potatoes. In the diagram, a sack of potatoes of mass 10 kg is resting on a scale that is resting on the floor of an accelerating elevator. The scale reads 12 kg. What is the acceleration of the elevator?



4 years ago Comment

Technically, if your question refers us to a diagram, then you owe us a peek at the
diagram. But there may be enough info in the description to solve this one blind.

Newton's second law of motion: F = M A
"The force on an object is the product of the object's mass and its acceleration."

Divide each side by 'A': A = F / M
"The rate at which an object accelerates is its mass divided by the force on it."
Hold that thought for a moment, while we go off on a tangent:
Everybody talks about "kg" as if it were a force, and this question shows why
that's a terrible thing to do.  In this question, "kg" is used BOTH as a mass AND
as a force. I can't think of a better way to confuse students who are just now
working with this stuff for the first time. The question is badly written, although,
in the real world, scales do read in 'kg'.
"Kg" is a mass. It is not a force.

I think that rather than try to teach more physics to get out of this hole,
the best way to go at it is like this:

If the scale were sitting still, on the ground, or rising at a steady rate and
not accelerating, then the only force on the 10 kg mass would be the force
of gravity, and the scale would read '10 kg'. But in the upward-accelerating
elevator, the scale reads 20% more, telling us that 20% more than the force
of gravity is acting on the mass. That extra 20% of upward force is provided
by the upward acceleration, which must be 20% of the acceleration of gravity.
The acceleration of gravity is 9.8 meters per second² .
The elevator is accelerating (0.2 x 9.8) = 1.96 meters per second².