When I asked my teacher for help he told me this
This is a logical puzzle. Having 75% of the typical weight means experiencing 75% of the typical gravity. The floor must be falling away with an acceleration of 25% of typical gravity.
Here's the question I asked that's from my textbook
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 person''s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.
ok isn't weight by defintion the force of gravity which is equal to mass time gravity how could this every change? I understand that in this situation the net force change but no the actual weight so I'm lost... I'm know the normal force exerted by the scale onto the person would change becasue the acceleration changes and for a brief moment weighs less than she would without going in the elevator...
so I'm the normal force exerted by the scale onto the person would obviously change but how would her weight change?
Can you explain to me how to do this problem or as to why I can do this problem this way because I do not understand it. Thanks
Her weight doesn't change, but her so-called "apparent weight" does change:
http://en.wikipedia.org/wiki/Apparent_weight
"how would her weight change?"
The force of weight we sense is actually the normal force, or the force pushing us up. If the elevator accelerates downward, that force is reduced, as is our perception of our weight.
By Newton's 3rd law, the sum of the forces acting on the person equals the mass times acceleration.
sum(F) = ma.
the sum of forces also equals the normal force + the force of weight.
sum(F) = Fn - Fw
When the person is at rest, the sum of the forces = 0.
0 = Fn - Fw
However, when the elevator accelerates downwards, the Fn is only .75 of what it was.
sum(F) = .75Fn + FW
ma = .75mg - mg
a = .75g - g
a = -.25g
I understand that you're confused about how weight can change in this scenario. Let me break it down for you and explain the concept.
Weight is the force with which an object is pulled towards the center of the Earth due to gravity. It is calculated as the product of mass and acceleration due to gravity (weight = mass * gravity). However, in situations like being in an elevator or any accelerating frame of reference, the apparent weight can be different from the actual weight because there are additional forces at play.
In this specific scenario, when the elevator starts to move, the person standing on the bathroom scale experiences a decrease in their apparent weight. This happens because the scale also exerts an upward force on the person, known as the normal force, to counterbalance the downward weight force. When the elevator accelerates, the normal force exerted by the scale is less than the person's actual weight, resulting in a lower reading on the scale.
To solve the problem, you need to find the acceleration of the elevator and its direction. Here's how you can approach it:
1. Recall that weight is equal to the product of mass and acceleration due to gravity: weight = mass * gravity.
2. In this case, the scale reads only 0.75 of the person's regular weight. So, you can represent the apparent weight as: 0.75 * person's regular weight.
3. Set up an equation using Newton's second law, which states that the net force acting on an object is equal to the product of its mass and acceleration: net force = mass * acceleration.
4. In the elevator, the net force is the difference between person's regular weight and the apparent weight. Therefore, you can write the equation as: person's regular weight - apparent weight = mass * acceleration.
5. Substitute the weight equation from step 1 and apparent weight from step 2 into the equation from step 4.
6. Solve the equation for acceleration. This will give you the magnitude of the elevator's acceleration.
7. Since the apparent weight is less than the regular weight, the direction of the acceleration should be in the upward direction. This is because the elevator is exerting a force in the upward direction to counterbalance the force of gravity.
By following these steps, you can calculate the acceleration and determine its direction in the given scenario.