The uniform disk of mass m 2 = 7.8 kg pivots freely on the cart of mass m 1 = 4.

Question

The uniform disk of mass m2 = 7.8 kg pivots freely on the cart of mass m1 = 4.1 kg. Determine the acceleration a of the assembly and the angular acceleration ? of the disk under the action of the force P = 64 N applied to a cord wrapped securely around the disk. The acceleration is positive if up the slope, negative if down. The angular acceleration is positive if counterclockwise, negative if clockwise.

The uniform disk of mass m2 = 7.8 kg pivots freely on the cart of mass m1 = 4.1 kg. Determine the acceleration a of the assembly and the angular acceleration ? of the disk under the action of the force P = 64 N applied to a cord wrapped securely around the disk. The acceleration is positive if up the slope, negative if down. The angular acceleration is positive if counterclockwise, negative if clockwise.

Explanation / Answer

We know the Force = mass x acceleration

acceleration of the assembly 64/(7.8+4.1)=5.3778 (along the direction of application of force)

in vector representation 5.3778 (cos16 i + sin 16 j)= 5.1698i + 1.4824j m/s^2

Moment of inertia of disk mr^2/2 = 0.22464 kg m^2

We know that torque = moment of inertia X angular acceleration

Torque = force x displacement =15.36 Nm

Angular acceleration = 68.37606 rad/s^2 (clockwise)

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