We consider the case shown in the figure below. Two objects with masses m and M are connected with a taut string running over a pulley. The pulley rotates without friction. The two masses are given as M = 6.23 kg and m = 2.54 kg. A second taunt string connects the heavier object vertically to the ceiling. Assume that both strings and the pulley are massless. Now we cut the string connecting the object with the mass M to the ceiling. Calculate the magnitude of the acceleration of mass M.
Without "the figure below", I just don't get the picture.
To calculate the magnitude of the acceleration of mass M, we need to analyze the forces acting on the system.
1. Gravity: Both masses (m and M) experience the force due to gravity. The force on the lighter mass m is given by F_m = m * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2). The force on the heavier mass M is F_M = M * g.
2. Tension: The tension in the string connecting the masses can be different on either side of the pulley because of the difference in mass. Let T1 be the tension in the string on the side of mass M, and T2 be the tension in the string on the side of mass m.
3. Acceleration: The magnitude of acceleration for both masses will be the same since they are connected by a string. We can denote this acceleration as a.
Now, let's consider the forces acting on mass M:
1. The force of gravity pulling mass M downward (F_M = M * g).
2. The tension in the string on the side of mass M (T1), which pulls mass M upward.
Since the string is cut, tension T1 will no longer exist after the cut. Therefore, the only force acting on mass M will be its weight, pulling it downward. This force causes mass M to accelerate.
We can use Newton's second law of motion to relate the force, mass, and acceleration:
F = m * a
In this case, F_M = M * g. Therefore, we have:
M * g = M * a
Simplifying the equation, we find:
a = g
So, the magnitude of the acceleration of mass M is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2.