A crane shown in the drawing is lifting a 170-kg crate upward with an acceleration of 1.8 m/s2. The cable from the crate passes over a solid cylindrical pulley at the top of the boom. The pulley has a mass of 130 kg. The cable is then wound onto a hollow cylindrical drum that is mounted on the deck of the crane. The mass of the drum is 150 kg, and its radius is 0.76 m. The engine applies a counterclockwise torque to the drum in order to wind up the cable. What is the magnitude of this torque? Ignore the mass of the cable.

Question

A crane shown in the drawing is lifting a 170-kg crate upward with an acceleration of 1.8 m/s2. The cable from the crate passes over a solid cylindrical pulley at the top of the boom. The pulley has a mass of 130 kg. The cable is then wound onto a hollow cylindrical drum that is mounted on the deck of the crane. The mass of the drum is 150 kg, and its radius is 0.76 m. The engine applies a counterclockwise torque to the drum in order to wind up the cable. What is the magnitude of this torque? Ignore the mass of the cable.

Can someone please help me!? Thank you

write the force equation Torque= ma/radiusdrum+ Ipulley*alphap + Idrum*alphad

Now on alphap, and alphad, that will be the acceleration of the cable/radius

Solve for Torque

chcek my thinking. THis is a thinkig problem.

Answer 1

Your thinking is correct. We can use the force equation Torque = ma/radius_drum + Ipulley * alphap + Idrum * alphad to solve for the magnitude of the torque.

Let's break down the equation:

Torque: This is the magnitude of the torque we want to find.

ma/radius_drum: This term represents the torque due to the acceleration of the crate. Since the crate is lifted upward with an acceleration of 1.8 m/s^2, we can substitute ma/radius_drum with (170 kg * 1.8 m/s^2) / radius_drum.

Ipulley * alphap: This term represents the torque due to the acceleration of the pulley. The moment of inertia of a solid cylindrical pulley is given by Ipulley = (1/2) * mass_pulley * radius_pulley^2. We can calculate alphap by dividing the acceleration of the crate (1.8 m/s^2) by the radius_pulley.

Idrum * alphad: This term represents the torque due to the acceleration of the drum. The moment of inertia of a hollow cylindrical drum is given by Idrum = (1/2) * mass_drum * (radius_outer_drum^2 - radius_inner_drum^2). We can calculate alphad by dividing the acceleration of the crate (1.8 m/s^2) by the radius_outer_drum.

By substituting these values into the equation and solving for Torque, we can find the magnitude of the torque exerted by the engine to wind up the cable.

Make sure to use the correct units for mass, acceleration, and radii to ensure consistent results.