Three identical 2kg blocks are free to move on a frictionless surface. The three blocks are connected by short massless cords and a force of 24 N is applied to the right most block.
1) find the accelerations of the 3 blocks
2) find the tensions in two cords connecting blocks
To find the accelerations of the three blocks, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the force applied and inversely proportional to its mass.
1) Acceleration of the blocks:
Since the blocks are identical and connected by cords, the force applied to the rightmost block will cause the entire system to accelerate together as a whole. Let's call this acceleration "a."
To determine the value of "a," we can use Newton's second law applied to the entire system. The total mass of the system is 2 kg + 2 kg + 2 kg = 6 kg, and the applied force is 24 N.
Using Newton's second law (F = m * a), we have:
24 N = 6 kg * a
Simplifying the equation, we find:
a = 24 N / 6 kg
a = 4 m/s²
Therefore, the acceleration of the three blocks is 4 m/s².
2) Tensions in the cords:
Since the blocks are connected by short massless cords, we can assume that the tension in the cords is constant throughout the system.
Let's label the three blocks as Block 1, Block 2, and Block 3 from left to right.
The tension in the cord between Block 3 and Block 2 will be the same since they are connected directly. Let's call this tension "T1."
Similarly, the tension in the cord between Block 2 and Block 1 will also be the same as T1. Let's call this tension "T2."
To find the tensions, we can consider the forces acting on each individual block:
For Block 1:
The only force acting on Block 1 is the tension in the cord between Block 1 and Block 2 (T2). This force is in the opposite direction of the applied force, so we can write:
T2 = m * a
Substituting the values, we get:
T2 = 2 kg * 4 m/s²
T2 = 8 N
For Block 2:
There are two forces acting on Block 2: the tension in the cord between Block 2 and Block 1 (T2) in the opposite direction of the applied force, and the tension in the cord between Block 2 and Block 3 (T1) in the same direction as the applied force. We can write:
T2 - T1 = m * a
Substituting the values, we get:
8 N - T1 = 2 kg * 4 m/s²
8 N - T1 = 8 N
T1 = 0 N
For Block 3:
The only force acting on Block 3 is the tension in the cord between Block 3 and Block 2 (T1) in the same direction as the applied force, so we can write:
T1 = m * a
Substituting the values, we get:
T1 = 2 kg * 4 m/s²
T1 = 8 N
Therefore, the tension in the cord between Block 2 and Block 1 (T2) is 8 N, and the tension in the cord between Block 3 and Block 2 (T1) is also 8 N.