Question
Calculate the tension and the acceleration on the masses hunged, one is 12kg and the other is 7.5 kg
Answers
GPT 3.5
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.
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.