When will your apparent weight be greatest, as measured by a a scale in a moving elevator; when the elevators: (a) accel. downward (b) accel. upward (c) is in free fall (d) moves upward at a constant speed? In what case would you weight be the least? When would it be the same as when you are on the ground?
Think about it.
weightapparent=mg+ma where a is up. What if a is down? What if a=-g?
Apparent weight
= m(g+a)
where g=9.8 m/s²
a=acceleration, positive upwards.
(a) W=m(g-|a|)
(b) W=m(g+|a|)
(c) W=m(g-|g|) = 0
(d) W=m(g+|0|) = mg
so the it would be the least on the way down, b/c your force, pushing on the scale is less. And it is greatest on the way up, since your force of push is stronger. And I would say in free fall it is the same as ground state?
Rethink free-fall.
ohh okay so the weight would be the same on the ground if its moving up at a constant speed?
Exactly. When it moves upwards (or downwards) at a uniform velocity, the reaction on the floor is the same as the weight. You have probably experienced this when you ride on an elevator.
sweet!! thank you =)
You're welcome!
To determine when your apparent weight is greatest, least, or the same as when you are on the ground in each scenario, we need to understand the concept of apparent weight in the context of an elevator.
(a) When the elevator accelerates downward:
In this case, your apparent weight will be greater than when you are on the ground. To understand why, we need to consider the forces acting on you. Your weight (mg) is always acting downward, but during downward acceleration, there is an additional force (ma) acting in the same direction. The scale in the elevator measures the sum of these forces, so your apparent weight will be greater.
(b) When the elevator accelerates upward:
Similar to the previous case, your apparent weight will be greater than when you are on the ground. The additional force (ma) due to the upward acceleration adds to your weight (mg) in this scenario as well, resulting in a greater apparent weight.
(c) When the elevator is in free fall:
In this scenario, the elevator and everything in it, including you, is falling freely under the influence of gravity. In free fall, there is no contact force between your feet and the floor of the elevator. As a result, the scale in the elevator will read zero, indicating that your apparent weight is zero. This condition is called weightlessness or zero apparent weight.
(d) When the elevator moves upward at a constant speed:
When the elevator moves upward at a constant speed, there is no acceleration involved. Therefore, there is no additional force acting on you. Your apparent weight in this scenario will be the same as your actual weight. Therefore, your apparent weight will be the same as on the ground.
To summarize:
- Greatest apparent weight: When the elevator is accelerating either downward or upward.
- Least apparent weight: When the elevator is in free fall or falling freely.
- Same apparent weight as on the ground: When the elevator is moving upward at a constant speed.