A lift of mass 1500 kg is raised by means of a rope passing round a drum of diameter 1.50 m. Given that the lift is accelerating upwards at 0.255 m s-2, draw a free body diagram of the lift, calculate the tension in the rope, the moment applied to the drum and the angular acceleration of the drum.
To draw a free body diagram of the lift, we need to consider all the forces acting on it.
1. Weight of the lift: This force acts vertically downwards and is given by the equation W = mg, where m is the mass of the lift and g is the acceleration due to gravity.
2. Tension in the rope: This force acts vertically upwards and is responsible for lifting the lift. We need to calculate this force.
Now, let's calculate the tension in the rope using Newton's second law of motion. The net force acting on the lift is given by the equation F_net = ma, where F_net is the net force, m is the mass of the lift, and a is the acceleration.
We can write the equation as follows:
T - W = m * a
Substituting the given values:
T - mg = (1500 kg) * (0.255 m/s^2)
To find the value of T, we need to know the acceleration due to gravity (g), which is approximately 9.8 m/s^2.
Calculating the tension in the rope:
T - (1500 kg * 9.8 m/s^2) = (1500 kg) * (0.255 m/s^2)
T - 14700 N = 382.5 N
T = 14700 N + 382.5 N
T = 15082.5 N
Therefore, the tension in the rope is 15082.5 N.
Next, let's calculate the moment applied to the drum. The moment (torque) applied to the drum is given by the equation M = Fr, where F is the force applied to the drum and r is the radius of the drum.
Since the force applied to the drum is the tension in the rope, we can substitute the value we calculated for T:
M = (15082.5 N) * (0.75 m)
Calculating the moment applied to the drum:
M = 11311.875 Nm
Therefore, the moment applied to the drum is 11311.875 Nm.
Lastly, let's calculate the angular acceleration of the drum. The angular acceleration (alpha) is given by the equation alpha = a/r, where a is the linear acceleration of the lift and r is the radius of the drum.
Substituting the given values:
alpha = (0.255 m/s^2) / (0.75 m)
Calculating the angular acceleration of the drum:
alpha = 0.34 rad/s^2
Therefore, the angular acceleration of the drum is 0.34 rad/s^2.