Three objects with masses
m1= 36.5 kg
m2= 19.2 kg
m3= 12.5 kg
Are hanging from massless ropes that run over a frictionless pulleys. If the system is released from rest, what is the magnitude of the acceleration in m/s^2 of mass m1?
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Three objects with masses m1= 36.5 kg m2= 19.2 kg m3= 12.5 kg Are hanging from massless ropes that run over a frictionless pulleys. If the system is released from rest, what is the magnitude of the acceleration in m/s^2 of mass m1?
To find the magnitude of the acceleration of mass m1, we need to analyze the forces acting on it.
First, let's consider the forces acting on mass m1. There are two forces acting on it: the tension in the rope pulling it upwards and the force of gravity pulling it downwards. The tension in the rope is the same throughout because the ropes are massless and there is no friction. The force of gravity on m1 is equal to its weight, which is given by the equation:
F_gravity = m1 * g
where m1 is the mass of m1 and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Next, let's determine the net force acting on m1. The net force is the vector sum of the forces acting on m1 and is given by the equation:
F_net = F_tension - F_gravity
Finally, we can use Newton's second law of motion to relate the net force to the acceleration of m1. Newton's second law states that the net force acting on an object is equal to the mass of the object times its acceleration:
F_net = m1 * a
where a is the acceleration of m1.
Setting these two equations equal to each other, we can solve for the acceleration:
m1 * a = F_tension - F_gravity
Substituting the expressions for F_tension and F_gravity and rearranging the equation, we get:
m1 * a = m1 * g - m1 * g
Simplifying further, we find that:
m1 * a = 0
Since m1 is not accelerating, the magnitude of the acceleration of m1 is 0 m/s^2.