A 50kg mass and a 85kg mass are hung over a frictionless pulley what is the acceleration of the system
To find the acceleration of the system when two masses are hung over a frictionless pulley, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a).
In this case, since the masses are connected by a rope and pulley system, they experience the same acceleration. Let's denote the acceleration as 'a', the mass of the first object as 'm1' (50 kg) and the mass of the second object as 'm2' (85 kg).
We need to calculate the net force acting on the system. The net force can be found by comparing the forces acting on the two masses. Here, the only force we need to consider is the force of gravity.
For mass m1, the force of gravity is given by F1 = m1 * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Similarly, for mass m2, the force of gravity is given by F2 = m2 * g.
Since the pulley is frictionless, the tension in the rope is the same on both sides of the pulley. Therefore, the net force acting on the system can be expressed as (F2 - F1).
Using Newton's second law, we can write the equation as (F2 - F1) = (m1 + m2) * a.
Substituting the known values, we get (85 * 9.8) - (50 * 9.8) = (50 + 85) * a.
This simplifies to (833 - 490) = 135 * a.
343 = 135 * a.
Finally, we can solve for 'a' by dividing both sides of the equation by 135:
a = 343 / 135.
Thus, the acceleration of the system is approximately 2.54 m/s².