A frictionless pulley with zero mass is attached to the ceiling, in a gravity field of 9.81 m/s2. Mass M2 = 0.15 kg is being accelerated downward at 1.5 m/s2.
Calculate the mass M1.
exactly how are the masses affixed to the pulley?
with massless strings
is mass1 and mass2 on opposite sides of the pulley?
To calculate the mass M1, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, the net force acting on mass M2 is equal to its mass multiplied by its acceleration. The net force is also equal to the tension in the string, which is pulling mass M2 upward, and is given by the weight of mass M1.
The weight of mass M1 is equal to its mass multiplied by the acceleration due to gravity, which is 9.81 m/s^2. Therefore, we have:
Tension = Weight of M1
m1 * g = m2 * a
Substituting the given values, we have:
M1 * 9.81 = 0.15 * 1.5
Now we can solve for M1:
M1 = (0.15 * 1.5) / 9.81
Calculating this expression gives us M1 ≈ 0.022 kg.