If you stand in a lift that is accelerating downwards at a rate of 2 m s-2, you will experience an apparent upthrust that acts against your weight. Your weight (the force that acts in a downward direction due to gravity) is:
W = m g
= mass x gravitational field strength
On Earth, g is about 9.8 N kg-1 or 9.8 m s-2 (both units are equivalent)
W = 50 kg x 9.8 N kg-1
= 490 N (in a downward direction)
The upward force due to your acceleration is given by Newton's second law:
F = m a
= mass x acceleration
= 50 kg x 2 m s-2
= 100 N (in an upward direction)
So the overall weight you feel is the difference between them. So:
W = 490 - 100
= 390 N
Yes, your weight appears to decrease slightly when an elevator goes down. This is because you and the elevator experience a decrease in acceleration as the elevator descends, which temporarily reduces the force acting on your body and hence, your perceived weight.
No, the scale will not have the same reading when you ascend and descend in the elevator. As the elevator ascends, the scale will show a higher weight due to the additional force from the acceleration of the elevator. Conversely, when the elevator descends, the scale will show a lower weight because of the deceleration. Thus, the readings will differ depending on the direction and acceleration of the elevator.
The acceleration of the elevator can be calculated by dividing the reading on the scale (836 N) by the student's mass to get the acceleration due to the elevator's motion. Additionally, the acceleration due to gravity should also be taken into account, as it will affect the weight measured by the scale.
If your weight increases while riding in an elevator, you are likely going upwards. As the elevator moves upwards, you experience a sensation of increased weight due to the acceleration.
If the elevator accelerates, the acceleration will provide an additional apparent force.
You weigh less only while the elevator's upward speed is decreasing, or downward speed is increasing. In each case, the acceleration of the elevator is in a direction opposite to the acceleration of gravity. The result of that is that the total acceleration acting on you is less than usual, and your weight is less. Note that in a sealed container, such as a space ship or an elevator, there's no way for you to tell the difference between acceleration and a gravitational field.
As the elevator begins to move upward, the reading on the scale will increase due to the increase in apparent weight experienced by the person inside the elevator. This increase is a result of the combination of the person's actual weight and the upward acceleration of the elevator.
That's the force that engineers call the "weight" of the elevator car. As long as the elevator stays on Earth, its weight is constant, whether it's rising, falling, stopped, or out of order. On or near the Earth's surface, the weight of 1,140 kilograms of mass is about 11,180 Newtons (2,513.3 pounds).
When you are in an elevator that starts from rest and accelerates upward, your weight (mass times gravitational acceleration) remains constant because your mass does not change. However, the normal force exerted by the floor increases during the upward acceleration. This is because the elevator's acceleration adds to the gravitational force, resulting in a greater normal force acting on you, which can be felt as an increase in apparent weight.
The elevator is accelerating downwards at g / 10 or ~3.2 ft/sec/sec (.98 m/sec/sec) note. the question shows that the weighing took place on a bathroom scale or a spring balance. If you used a beam balance or a steelyard you would always measure 100lbs.
When an elevator accelerates upward from rest, your weight (the force due to gravity acting on you) remains constant, as it is determined by your mass and the acceleration due to gravity. However, the normal force exerted by the floor increases because it must counteract both your weight and provide additional force due to the upward acceleration of the elevator. Consequently, you would feel heavier during the upward acceleration, as the normal force exceeds your weight.
The solution to the elevator physics problem involves understanding the forces acting on the elevator and applying Newton's laws of motion. By considering the weight of the elevator and the tension in the cables, one can determine the acceleration and motion of the elevator.