The three blocks shown are released from rest and are observed to move with accelerations that have a magnitude of 1.5 m/s2. Disregard any pulley mass or friction in the pulley and let M = 2 kg. What is the tension force between M and 2M?
Imagine that the * does exist to see the real figure of the three block conect by the string and pulley.
pullet---block2M---pulley
***l********************l
***l********************l
***l********************l
blockM block 2M
The three blocks shown are released from rest and are observed to move with accelerations that have a magnitude of 1.5 m/s2. Disregard any pulley mass or friction in the pulley and let M = 2 kg. What is the tension force between M and 2M?
Imagine that the * does exist to see the real figure of the three block conect by the string and pulley.
pullet---block2M---pulley
***l********************l
***l********************l
***l********************l
blockM ************block 2M
To find the tension force between block M and block 2M, we can use Newton's second law of motion, which states that the sum of the forces acting on an object is equal to the mass of the object multiplied by its acceleration.
Let's break down the forces acting on each block separately:
For block M:
1. The tension force pulling block M upwards.
2. The force of gravity acting downwards, which is equal to the mass of block M multiplied by the acceleration due to gravity (9.8 m/s^2).
For block 2M:
1. The tension force pulling block 2M downwards.
2. The force of gravity acting downwards, which is equal to the mass of block 2M multiplied by the acceleration due to gravity (9.8 m/s^2).
Now, let's apply Newton's second law to each block:
For block M:
Tension force - (mass of M * acceleration) = 0 (since it is at rest)
For block 2M:
(mass of 2M * acceleration) - Tension force - (mass of 2M * acceleration due to gravity) = 0
Solving these two equations simultaneously will give us the tension force between block M and block 2M.
Let's substitute the given values into the equations:
- The mass of M is 2 kg.
- The mass of 2M is 4 kg.
- The acceleration is given as 1.5 m/s^2.
For block M:
T - (2 kg * 1.5 m/s^2) = 0
For block 2M:
(4 kg * 1.5 m/s^2) - T - (4 kg * 9.8 m/s^2) = 0
Now, you can solve these two equations to find the tension force (T) between block M and block 2M.