A frictionless pulley with zero mass is attached to the ceiling. Mass M2 = 0.140 kg is being accelerated downward with 1.30 m/s2. Calculate the mass m1.
To calculate the mass m1, we can set up an equation using Newton's second law.
First, let's determine the forces acting on the masses.
For mass M2:
The force acting on it is its weight, which can be calculated as M2 * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2). So the force acting on M2 is F2 = M2 * g.
Next, let's determine the force acting on mass m1.
Since the pulley is frictionless and massless, the tension in the rope is the same on both sides. Therefore, the force acting on m1 is also F2 = M2 * g.
Now, let's apply Newton's second law to the masses individually:
For mass M2:
F2 = M2 * a2,
where a2 is the acceleration of M2, given as 1.30 m/s^2.
Now, let's apply Newton's second law to mass m1:
F2 = m1 * a1,
where a1 is the acceleration of m1.
Since the force acting on both masses is the same, we can write:
M2 * a2 = m1 * a1.
Substituting the given values, we have:
0.140 kg * 1.30 m/s^2 = m1 * a1.
Simplifying the equation, we find:
0.182 kg m/s^2 = m1 * a1.
To find the value of m1, we need to know the acceleration, a1. The problem doesn't provide that information, so we cannot solve for m1 with the given data.