A string that passes over a pulley has a 0.331g mass attached to one end and a 0.625g mass attached to the other end. The pulley, which is a disk of radius 9.50cm , has friction in its axle.
What is the magnitude of the frictional torque that must be exerted by the axle if the system is to be in static equilibrium?
Difference in mass, Δm
= 0.625-0.331 g
= 0.294/1000 kg
= 0.000294 kg
Radius, r
= 9.5 cm
= 0.095 m
Torque required
=Δm * r Nm
F=mv^2/r v=u^2+2as
To find the magnitude of the frictional torque exerted by the axle, we need to consider the forces acting on the system and the rotational motion. To achieve static equilibrium, the net force and net torque must both be zero.
Let's break down the problem step by step:
1. Determine the forces acting on the system: In this case, there are two forces acting on the system - the force due to the tension in the string and the force due to the friction at the axle.
2. Calculate the force due to the tension: The force due to tension is equal to the weight of the masses. We can find this by using the formula: force = mass * acceleration due to gravity. So, the force due to tension on the 0.331g mass is (0.331g) * (9.8 m/s^2), and on the 0.625g mass is (0.625g) * (9.8 m/s^2).
3. Calculate the torque due to the tension: Torque is the perpendicular force multiplied by the distance from the axis of rotation. In this case, the radius of the pulley is given as 9.50cm, which is equal to 0.095m. The torque due to the tension on the 0.331g mass is (force due to tension) * (distance from the axis of rotation), and on the 0.625g mass is (force due to tension) * (distance from the axis of rotation).
4. Establish the equation for static equilibrium: In static equilibrium, the net force and the net torque must both be zero. So, we can sum up the forces and torques acting on the system.
5. Solve for the magnitude of the frictional torque: Since the net torque is zero in static equilibrium, the magnitude of the frictional torque exerted by the axle must be equal to the torque due to the tension on the masses.
By following these steps and performing the calculations, you can find the magnitude of the frictional torque exerted by the axle.