Two blocks of mass m = 14.9 kg each are fastened to the ceiling of an elevator,The elevator accelerates upward at a = 1.62 m/s2. Find the tension in the bottom rope and the top of the rope.

To find the tension in the bottom rope and the top of the rope, we need to consider the forces acting on the blocks.

Let's start by identifying the forces on each block:

1. Block 1 (at the bottom):
- Weight force (mg) acting downward.
- Tension force (T1) acting upward from the bottom rope.

2. Block 2 (on top):
- Weight force (mg) acting downward.
- Tension force (T2) acting upward from the top rope.

Since both blocks are fastened to the ceiling of the elevator, their weights (mg) cancel each other out. Therefore, we don't need to consider the weight forces in our calculation.

Now, let's analyze the forces acting on the two blocks due to the acceleration of the elevator.

1. Block 1:
- Tension force (T1) acting upward.
- Force of inertia (ma) acting downward due to the acceleration (a) of the elevator.

2. Block 2:
- Tension force (T2) acting upward.
- Force of inertia (ma) acting downward due to the acceleration (a) of the elevator.

To calculate the tensions (T1 and T2), we can use Newton's second law, which states that the net force (resultant force) acting on an object is equal to its mass times acceleration (F_net = ma).

For Block 1:
T1 - ma = 0 (since the block is not accelerating relative to the elevator)
Therefore, T1 = ma

For Block 2:
T2 - ma = 0 (since the block is not accelerating relative to the elevator)
Therefore, T2 = ma

Substituting the acceleration value (a = 1.62 m/s^2) and the mass of the blocks (m = 14.9 kg) into the above equations:

T1 = m * a = 14.9 kg * 1.62 m/s^2 = 24.078 N
T2 = m * a = 14.9 kg * 1.62 m/s^2 = 24.078 N

Hence, the tension in the bottom rope (T1) is 24.078 N, and the tension in the top rope (T2) is also 24.078 N.