a person stands on a bathroom scale in a motionless elevator. when the elevator begins to move, the scale briefly reads only .75 of the persons regular wieght. calculate the acceleration of the elevator, and find the direction of acceleration.(ans 2.5 m/s^2, and down) confused on how to start this problem, need help!!!!
weightonscale=weight(1+acceleration/g) where g is 9.8m/s^2, you maybe using 10m/s^2 as an ridiculous approximation. Nowhere on Earth is the acceleration due to gravity 10m/s^2, but apparently your text does.
Here, you are given weightonscale/weight= .75, so
.75=(1+acceleration/g)
acceleration will be negative, which means downward.
Typically, Sarah, the acceleration on an elevator is about .5m/s^2 max, either up or down. Changes faster than this make people have fits of nausea.
http://hypertextbook.com/facts/2005/elevator.shtml
To solve this problem, we can use the equation:
weight_on_scale = weight * (1 + acceleration/g)
where weight_on_scale is the reading on the scale, weight is the actual weight of the person, acceleration is the acceleration of the elevator, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
In this case, we are given weight_on_scale = 0.75 * weight. Plugging this into the equation, we get:
0.75 * weight = weight * (1 + acceleration/g)
To find the acceleration, we can rearrange the equation:
0.75 = 1 + acceleration/g
Now, let's solve for acceleration:
0.75 - 1 = acceleration/g
-0.25 = acceleration/g
Next, we can multiply both sides of the equation by g to isolate the acceleration:
acceleration = -0.25 * g
Since g is positive (the acceleration due to gravity), the acceleration will be negative. This means the elevator is accelerating downward.
Now, let's substitute the value of g (approximately 9.8 m/s^2) into the equation:
acceleration = -0.25 * 9.8 = -2.45 m/s^2
Therefore, the acceleration of the elevator is approximately -2.45 m/s^2 (rounded to 2 decimal places), and it is accelerating downward.