A pulley is holding two masses-0.5 kg and 2.0 kg. The system is in static equilibrium; the pulley is frictionless; the string is massless.
What is the tension of the string holding the pulley?
If the system is in static equilibrium, there is no motion for any of the items.
So the tension of the string holding the pulley is
Ī£mass*acceleration due to gravity
=(0.5kg+2.0kg+0kg(string)+mass of pulley)*g
=(2.5kg+mass of pulley)*g
To determine the tension in the string holding the pulley, we need to consider the forces acting on the two masses connected by the string.
Let's designate the 0.5 kg mass as m1 and the 2.0 kg mass as m2. Since the system is in static equilibrium, the forces on both masses must balance out.
For m1: The only force acting on m1 is its own weight (mg1), where g is the acceleration due to gravity (approximately 9.8 m/s^2). Therefore, the tension in the string will be equal to the weight of m1.
Tension in the string (T) = Weight of m1 (mg1)
For m2: The force acting on m2 is its own weight (mg2) in the downward direction and the tension in the string (T) in the upward direction.
Since the system is in equilibrium, these two forces must be equal and opposite, meaning:
mg2 = T
Therefore, the tension in the string holding the pulley is equal to the weight of m2.
Now we can calculate the tension knowing the masses:
Weight of m1 = m1 * g = 0.5 kg * 9.8 m/s^2
Weight of m2 = m2 * g = 2.0 kg * 9.8 m/s^2
Since the tension in the string is the same for both masses, we can conclude that the tension in the string holding the pulley is equal to the weight of m2:
Tension in the string (T) = Weight of m2 = 2.0 kg * 9.8 m/s^2
Tension in the string (T) = 19.6 N