The blocks are pulled to the right and accelerate with a magnitude of 1.1 m/s^2. If mass 1 is 4.0 kg, mass 2 is 2.3 kg, and mass 3 is 3.4 kg, calculate the tension in each string. Assume that friction is negligible.

Answer 1

To calculate the tension in each string, we can apply Newton's second law to each block individually.

For mass 1:
The net force acting on mass 1 is the tension in the first string, T1, to the right, minus the weight of mass 1, mg, to the left. Since the weight of an object on Earth is given by the formula mg, where g is the acceleration due to gravity (approximately 9.8 m/s^2), the weight of mass 1 is 4.0 kg × 9.8 m/s^2 = 39.2 N.

Using Newton's second law, F = ma, where F is the net force acting on an object of mass m and resulting in an acceleration a, we have:
T1 - 39.2 N = (4.0 kg)(1.1 m/s^2)
T1 - 39.2 N = 4.4 N
T1 = 4.4 N + 39.2 N
T1 = 43.6 N

For mass 2:
The net force acting on mass 2 is the tension in the second string, T2, to the right, minus the weight of mass 2, mg, to the left. The weight of mass 2 is 2.3 kg × 9.8 m/s^2 = 22.54 N.

Using Newton's second law, F = ma, we have:
T2 - 22.54 N = (2.3 kg)(1.1 m/s^2)
T2 - 22.54 N = 2.53 N
T2 = 2.53 N + 22.54 N
T2 = 25.07 N

For mass 3:
The net force acting on mass 3 is the tension in the third string, T3, to the right, minus the weight of mass 3, mg, to the left. The weight of mass 3 is 3.4 kg × 9.8 m/s^2 = 33.32 N.

Using Newton's second law, F = ma, we have:
T3 - 33.32 N = (3.4 kg)(1.1 m/s^2)
T3 - 33.32 N = 3.74 N
T3 = 3.74 N + 33.32 N
T3 = 37.06 N

Thus, the tension in string 1 (T1) is 43.6 N, the tension in string 2 (T2) is 25.07 N, and the tension in string 3 (T3) is 37.06 N.