A person stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.74 of the person's regular weight.
Calculate the magnitude of acceleration of the elevator.
Find the direction of acceleration and why.
The weight registered on the scale will show zero if the elevator is in free-fall.
If the elevator is accelerating downwards, the scale will register less than the actual weight.
Let m=mass of the person,
a=acceleration downwards,
g=acceleration due to gravity, 9.8 m/s/s
then
net force on the scale
=m(a-g)=0.74mg
a-g = 0.74g
a=(1-0.74)g=0.26g m/s/s
To calculate the magnitude of acceleration of the elevator, we need to use the concept of apparent weight. Apparent weight is the reading on a scale when an object is accelerating or decelerating.
Let's assume the person's regular weight is denoted as W (in Newtons). When the elevator is at rest, the scale measures the person's regular weight, which is W.
When the elevator begins to move, the scale reads only 0.74 of the person's regular weight. This means that the scale is measuring 0.74W.
To find the magnitude of acceleration, we need to calculate the difference between the two weights.
Difference in weight = Apparent weight - Regular weight
= 0.74W - W
= (0.74 - 1)W
= -0.26W
Since weight is a force and force is mass multiplied by acceleration (F = m * a), we can rewrite the difference in weight equation as:
-0.26W = m * a
Where m is the mass of the person and a is the acceleration of the elevator. We can cancel out the mass (m) from both sides of the equation and solve for the acceleration (a):
a = -0.26W / m
To find the direction of acceleration, we can look at the magnitude of the difference in weight (-0.26W). Since the scale reads a lower weight than the regular weight, we can conclude that the elevator is accelerating downwards. Therefore, the direction of acceleration is downwards.
In conclusion, to find the magnitude of acceleration, you'll need the person's regular weight (W) and the mass of the person. Plug these values into the equation a = -0.26W / m. The direction of acceleration is downwards because the scale reads a lower weight than the regular weight.