The formula for calculating acceleration in a vertical pulley system is a = (m1 - m2)g / (m1 + m2), where m1 is the mass of the hanging weight and m2 is the mass of the counterweight.
To determine the tension in the rope, you can use the formula T = m1a + m1g, where T is the tension, m1 is the mass of the hanging weight, a is the acceleration, and g is the acceleration due to gravity.
If the mass of the hanging weight is increased, the acceleration of the system will decrease. This is because the increased weight will cause a larger force to be exerted on the counterweight, resulting in a slower acceleration.
If the mass of the counterweight is increased, the acceleration of the system will increase. This is because the increased weight will cause a larger force to be exerted on the hanging weight, resulting in a faster acceleration.
Yes, the acceleration of a vertical pulley system can be affected by friction. If there is friction present in the pulley or on the surface where the rope is moving, it can decrease the acceleration of the system by adding a counteracting force. However, this effect is often negligible in simple pulley systems.