a) 784.5 N
b) 47.8 N
Explanation:
a)
Find the free-body diagram of the person in attachment.
There are two forces acting on the person:
- Its weight (gravitational force), of magnitude W = 625 N, downward
- The normal reaction exerted by the scale on the person, upward, of magnitude N: this corresponds to the reading on the scale
Therefore, the net upward force on the person is
According to Newton's second law of motion, the net force must be equal to the product of mass and acceleration, so:
where:
is the mass of the person
is the acceleration of the elevator (upward)
Re-arranging the equation and solving for N, we can find the reading on the scale (the normal force):
b)
In this case, you are holding a package of 3.85 kg with a light string.
The forces acting on the package are:
- The weight (force of gravity), , downward
- The tension in the string, T, upward
As before, the net force on the package is
And according to Newton's second law, it must be equal to the product of mass and acceleration:
Therefore here we have:
m = 3.89 kg is the mass
is the acceleration due to gravity
is the acceleration of the elevator
Solving for T, we find the tension in the string: