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
[tex]F=N-W[/tex]
According to Newton's second law of motion, the net force must be equal to the product of mass and acceleration, so:
[tex]F=N-W=ma[/tex]
where:
[tex]m=\frac{W}{g}=\frac{625}{9.8}=63.8 kg[/tex] is the mass of the person
[tex]a=2.50 m/s^2[/tex] 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):
[tex]N=ma+W=(63.8)(2.50)+625=784.5 N[/tex]
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), [tex]W=mg[/tex], downward
- The tension in the string, T, upward
As before, the net force on the package is
[tex]F=T-W=T-mg[/tex]
And according to Newton's second law, it must be equal to the product of mass and acceleration:
[tex]T-mg=ma[/tex]
Therefore here we have:
m = 3.89 kg is the mass
[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity
[tex]a=2.50 m/s^2[/tex] is the acceleration of the elevator
Solving for T, we find the tension in the string:
[tex]T=m(a+g)=(3.89)(2.50+9.8)=47.8 N[/tex]
