Understanding Tension and Weight in Elevators: Newton's Laws Homework

In summary, the relation between the tension in the cable, T, and the weight of the ball, Mg, varies in different situations. In the first two scenarios, T is greater than mg due to the downward acceleration of the elevator. In the third scenario, T equals mg as the elevator is stationary. In the fourth scenario, T is greater than mg as the elevator is accelerating upwards. In the fifth scenario, T equals mg as the elevator is traveling at a constant velocity. And in the sixth scenario, T is less than mg as the elevator is accelerating downwards.
  • #1
BuBbLeS01
602
0

Homework Statement


A ball of mass M is suspended by a thin string (of negligible mass) from the ceiling of an elevator. The vertical motion of the elevator as it travels up and down is described in the statements below. Indicate for each of the situations described the relation between value of the tension in the cable, T, and the weight of the ball, Mg, or whether one Cannot tell.
(Assume that there is no air, i.e., neglect the buoyancy effect of the air.)

The elevator is traveling upward and its upward velocity is decreasing as it nears a stop at a higher floor.

The elevator is traveling downward and its downward velocity is decreasing as it nears a stop at a lower floor.

The elevator is stationary and remains at rest.

The elevator is traveling upward and its upward velocity is increasing as it begins its journey towards a higher floor.

The elevator is traveling upward at a constant velocity.

The elevator is traveling downward and its downward velocity is increasing

The Attempt at a Solution


1. T>mg
2. T>mg
3. T=mg
4. T<mg
5. T=mg
6. T<mg

Where am I going wrong? My answers are not right, but I am not sure where my mistake(s) are.
 
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  • #2
Draw diagrams showing a ball and three things: the tension, the weight, and the acceleration. Apply Newton's 2nd law F=ma and try to deduce the relations.
 
  • #3
Take the first one:
In this case, acceleration is DOWNWARDS, in the direction of the force of gravity.
Now, does that mean the upwards tension force is greater or less than the weight of the mass?
 
  • #4
less than
 
  • #5
Quite so!
Now, give an argument as to why you think 2. is correct.
 
  • #6
because the acceleration is acting upwards, opposite of gravity so the tension force would be greater
 
  • #7
Correct!

Now, study your other answers, present your arguments for your view; you are allowed to change your mind if you think you made some mistake earlier.
 
  • #8
Thank you!
 
  • #9
You are not finished..:smile:
 
  • #10
I know I am working on them... I know the third has to be equal and the 4th I think T would be greater because it is accelerating upwards, opposite of gravity
 
  • #11
BuBbLeS01 said:
I know I am working on them... I know the third has to be equal and the 4th I think T would be greater because it is accelerating upwards, opposite of gravity
You are right; only a "surplus" of tensile force can yield upwards acceleration.

The other relations are right.
 
  • #12
okay thanks so much!
 

1. What are Newton's Laws of Motion and how do they relate to elevators?

Newton's Laws of Motion are three fundamental principles that describe the behavior of objects in motion. They relate to elevators by explaining the forces at play in an elevator and how they affect the movement of the elevator and its occupants.

2. How does the first law of motion apply to elevators?

The first law, also known as the law of inertia, states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. In elevators, this means that if the elevator is not moving, it will remain stationary unless an external force (such as the elevator motor) acts on it. If the elevator is already moving at a constant speed, it will continue to move unless an external force (such as the brakes) slows it down.

3. How does the second law of motion apply to elevators?

The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In elevators, this means that the heavier the elevator and its occupants, the more force (in the form of the elevator motor) is needed to accelerate it upwards or downwards. This is why elevators may feel heavier when they are full of people compared to when they are empty.

4. What is the significance of the third law of motion in elevators?

The third law states that for every action, there is an equal and opposite reaction. In elevators, this means that when the elevator moves up or down, there is an equal and opposite force acting on the occupants. This is why we feel a slight push or pull when the elevator starts or stops moving.

5. How do Newton's Laws of Motion affect the safety and design of elevators?

Understanding Newton's Laws of Motion is crucial in the design and operation of elevators to ensure their safety. Engineers use these laws to calculate the necessary forces and materials needed to safely move elevators and their occupants. Additionally, the laws also help in the development of safety features such as emergency brakes and overload sensors to prevent accidents and ensure the smooth functioning of elevators.

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