A string is wrapped around a uniform solid cylinder of radius 3.10 cm, as shown in the figure. The cylinder can rotate freely about its axis. The loose end of the string is attached to a block. The block has mass 16.3 kg, and the cylinder has mass 11.2 kg.
and the question is.....
To find the tension in the string, we need to consider the forces acting on the block and the cylinder.
1. Weight of the block:
The weight of the block acts downwards and can be calculated using the formula:
Weight = mass * acceleration due to gravity
Weight of the block = 16.3 kg * 9.8 m/s^2
2. Tension in the string:
The tension in the string is the force that keeps the block and the cylinder in equilibrium. It can be calculated by considering the torques acting on the system.
The torque exerted by the weight of the block is given by:
Torque_block = (weight of the block) * (radius of the cylinder)
The torque exerted by the tension in the string is given by:
Torque_string = (tension in the string) * (radius of the cylinder)
Since the cylinder is uniform and can rotate freely, the torques must be equal and opposite to maintain equilibrium:
Torque_block = Torque_string
Substituting the values, we can solve for the tension in the string.
3. Weight of the cylinder:
The weight of the cylinder also acts downwards and can be calculated using the formula:
Weight_cylinder = mass_cylinder * acceleration due to gravity
Weight of the cylinder = 11.2 kg * 9.8 m/s^2
Once we have the tension in the string, we can also calculate the net force acting on the system by adding up the weight of the block and the weight of the cylinder and equating it to the tension in the string:
Net force = Weight of the block + Weight of the cylinder = tension in the string
This calculation allows us to find the tension in the string when a block is attached to a uniform solid cylinder that can rotate freely about its axis.