(a) (downward)
The equation of the forces acting on the student is:
(1)
where
N is the normal reaction of the scale on the student
mg is the weight of the student
a is the acceleration of the student
The scale reads 450 N, so this is the normal reaction:
N = 450 N
Also, we know that the weight of the student is:
So we can find its mass:
So now we can solve eq.(1) to find the acceleration:
where the negative sign means the acceleration is downward.
(b) , upward
Again, the equation of the forces is
where this time, the reading of the scale (and so, the normal reaction) is
N = 670 N
Solving for the acceleration, we find
and the positive sign means the acceleration here is upward.
(c) Yes
Let's assume the scale is reading zero. In terms of forces, this means that the normal reaction on the student is zero:
N = 0
So the equation of the forces simply becomes
Therefore the acceleration is
which means that the elevator is accelerating downward at : this means that the elevator is in free fall, so yes, the student should worry.
(d) (a) 6817 N
Let's now consider the equation of the forces on the elevator:
(2)
where this time:
T is the tension in the cable
is the weight of the elevator+student system
is the acceleration
Solving for T,
(d) (b) 10149 N
Here we can use the same equation
where the only difference is that the acceleration is
Solving the equation for T, we find
(d) (c) 0
Again, same equation
But this time, the acceleration is
So, we find:
So, the tension in the cable is zero, since the elevator is in free fall.