Calculate the tension and the acceleration on the masses hunged, one is 12kg and the other is 7.5 kg

Answer 1

To calculate the tension and acceleration of the masses, we will need to consider the forces acting on each mass.

Given:
Mass 1 = 12 kg
Mass 2 = 7.5 kg
Acceleration due to gravity (g) = 9.81 m/s^2

Step 1: Calculate the total force acting on each mass (weight):
Weight of Mass 1 = 12 kg * 9.81 m/s^2 = 117.72 N
Weight of Mass 2 = 7.5 kg * 9.81 m/s^2 = 73.57 N

Step 2: Calculate the tension in the string:
Let T be the tension in the string.

For Mass 1:
T - 117.72 N = 12 kg * a (where a is the acceleration)
T - 117.72 = 12a (equation 1)

For Mass 2:
117.72 N - T = 7.5 kg * a
117.72 - T = 7.5a (equation 2)

Step 3: Solve the system of equations:

Substitute equation 1 into equation 2:
117.72 - (117.72 - 12a) = 7.5a
117.72 - 117.72 + 12a = 7.5a
12a = 7.5a
4.5a = 117.72
a ≈ 26.16 m/s^2

Step 4: Calculate the tension in the string:
Using equation 1:
T - 117.72 = 12 * 26.16
T - 117.72 = 313.92
T ≈ 431.64 N

Therefore, the tension in the string is approximately 431.64 N and the acceleration of the masses is approximately 26.16 m/s^2.