In a system with a 2 kg mass and a 5 kg mass connected by a cord over a pulley, what is the acceleration of the masses after they are released?

• A. g
• B. 2g/7
• C. 3g/7
• D. 5g/7

Answer: (C)

To determine the acceleration of the system comprising two masses connected over a pulley, we can apply Newton's second law of motion. The key here is to set up the forces acting on both masses and derive the resultant acceleration.

Let’s denote the mass of one object as m1 (2 kg) and the other as m2 (5 kg). When the masses are released, m2 (the heavier mass) will accelerate downward, while m1 will move upward. The gravitational force acting downward on each mass can be described as follows:

• The force on m1 (2 kg) is: (F_{m1} = m1 \cdot g = 2g).

• The force on m2 (5 kg) is: (F_{m2} = m2 \cdot g = 5g).

When applying Newton's second law to the system, we consider the net force acting on the system. The net force can be determined by the difference in gravitational forces acting on the two masses:

[ F_{net} = F_{m2} - F_{m1} = 5g - 2g = 3g. ]

The total mass being accelerated is the sum of both masses