Two masses, 5 kg and 8 kg, are connected by a string passing over a pulley. If the system is released from rest, calculate the acceleration of the masses and the tension in the string.
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To calculate the acceleration of the masses and the tension in the string, we can use Newton's second law of motion.
Let's assume that the 5 kg mass is hanging vertically downward, and the 8 kg mass is on a horizontal surface.
The forces acting on the 5 kg mass are its weight (m1*g, where g is the acceleration due to gravity) and the tension in the string (T). Since the 5 kg mass is hanging vertically, the net force acting on it is given by:
F1 = m1 * g - T
The forces acting on the 8 kg mass are its weight (m2 * g) and the tension in the string (T). Since the 8 kg mass is on a horizontal surface, the net force acting on it is given by:
F2 = T - m2 * g
The tension in the string is the same for both masses, so we can set F1 equal to F2:
m1 * g - T = T - m2 * g
Simplifying this equation, we get:
2T = (m1 + m2) * g
Now we can substitute the given values:
2T = (5 kg + 8 kg) * 9.8 m/s^2
2T = 13 kg * 9.8 m/s^2
2T = 127.4 N
Dividing both sides by 2, we find the tension in the string:
T = 63.7 N
To find the acceleration of the masses, we can use the equation:
F2 - F1 = (m1 + m2) * a
Since F2 - F1 = 2T, we get:
2T = (m1 + m2) * a
Substituting the given values, we find:
2 * 63.7 N = (5 kg + 8 kg) * a
127.4 N = 13 kg * a
Dividing both sides by 13 kg, we find the acceleration:
a = 9.8 m/s^2
Therefore, the acceleration of the masses is 9.8 m/s^2, and the tension in the string is 63.7 N.
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