Why Is the Tension Different in Each Rope of an Accelerating Elevator?

[starfish794]

Two blocks are fastened to the ceiling of an elevator. The elevator accelerates upward at 1.70 m/s2. The blocks both have a mass of 11.5 kg. Find the tension in each rope.


______________________
....|
....|
....|
...__________
...|...|
...|...|
....|
....|
....|
...__________
...|...|
...|...|

I'm stuck. It seems like the tension on both ropes should be the same but its not.

 

[Astronuc]

Think of what the problem would be without the elevator stopped.

There are two blocks of mass m1 (upper mass) and m2 (lower mass). The bottom rope supports the weight of m2, which is m2*g. The top (upper) rope supports weights of both blocks m1* g + m2 * g = (m1+m2)*g.

Now what must one do to adjust the acceleration g if elevator is accelerating upward at 1.7 m/s²?

 

[kyle8921]

I can provide a mathematical explanation for the different tension in each rope. Firstly, we need to understand that the tension in a rope is caused by the force being applied to it. In this case, the force is due to the acceleration of the elevator, which is 1.70 m/s2.

Using Newton's Second Law (F=ma), we can calculate the force acting on each block. Since both blocks have a mass of 11.5 kg, the force on each block would be 11.5 kg x 1.70 m/s2 = 19.55 N.

Now, let's consider the forces acting on each block. The block on the left is being pulled upwards by the tension in the rope, and also being pulled downwards by its weight (mg). The block on the right is only being pulled downwards by its weight (mg).

Using Newton's Third Law (for every action, there is an equal and opposite reaction), we know that the tension in the rope is equal to the weight of the block on the left minus the weight of the block on the right.

Therefore, the tension in the left rope would be (19.55 N + 11.5 kg x 9.8 m/s2) = 129.9 N. And the tension in the right rope would be (11.5 kg x 9.8 m/s2) = 112.7 N.

In conclusion, the tension in each rope is different because of the different forces acting on each block. The block on the left has an additional force (its own weight) acting on it, resulting in a higher tension in the rope. I hope this explanation helps to clear up any confusion.