Tension of strings in an elevator

[sodaMay]

Two masses are connected by a string and are hanging from the ceiling of an elevator like this:

[string 1]
|
[4kg mass]
|
[string 2]
|
[6kg mass]

Show the tension of each string in the following situations:
i) Stationary
ii) Moving up at 3m/s
iii) Moving down at 3m/s
iv) Moving up at 3m/s/s
v) Moving down at 3m/s/s

Ok, I am kinda stumped. Where do I start? Is there a formula for tension? Is it F=ma? Or F=m(9.8-a) or something?

I'm just so horrible at physics, I'll be so grateful if someone could explain how this works..

Thanks! :)

 

[Dr. Jekyll]

You just need to look at the net force on each string. For example, you have two forces on the first string (weights of the hanging bodies). Other one is even easier. Remember the 1st Newton's law. That's when the elevator is stationary.

The formula $F=ma$ can be used in part (iv) and (v). It's the inertial force. Just be aware of its direction.

 

[Moetasim]

First of all, don't worry, you're not alone in feeling overwhelmed by physics! It can definitely be a challenging subject, but with some practice and understanding of the basic principles, it can become much easier to grasp.

To answer your question, yes, there is a formula for tension. It is typically represented as T and is equal to the force applied to a string or rope, which in turn creates tension in the string. The formula for tension is T=mg, where m is the mass of the object and g is the acceleration due to gravity (9.8 m/s^2 on Earth).

Now, let's apply this formula to the situation described above. In all of the following situations, the mass of the 4kg object will be represented as m1 and the mass of the 6kg object will be represented as m2.

i) Stationary: In this situation, the elevator is not moving, so there is no acceleration. Therefore, the tension in each string will simply be equal to the weight of the objects hanging from them. For string 1, the tension will be T1=m1g=(4kg)(9.8 m/s^2)=39.2 N. Similarly, for string 2, the tension will be T2=m2g=(6kg)(9.8 m/s^2)=58.8 N.

ii) Moving up at 3m/s: In this situation, the elevator is moving up at a constant velocity of 3m/s. This means that the acceleration is 0, so the formula for tension remains the same. The only difference is that the weight of the objects will be slightly reduced due to the upward motion. The tension in each string will be T1=m1g=(4kg)(9.8 m/s^2-3 m/s)=19.6 N and T2=m2g=(6kg)(9.8 m/s^2-3 m/s)=29.4 N.

iii) Moving down at 3m/s: This situation is essentially the same as the previous one, except now the elevator is moving down at a constant velocity of 3m/s. The tension in each string will be T1=m1g=(4kg)(9.8 m/s^2+3 m/s)=58.8 N and T2=m2g=(6kg)(9.8 m/s^2+3 m/s)=88.