Question

A laboratory freight elevator, including its load, has a mass of 500 kg. It is prevented from rotating by the track and wheels mounted along its sides. The elevator is used to carry highly sensitive equipment so it cannot exceed an acceleration of 3 m/s2 . A geared motor is used with the cable/pulley system shown below to raise and lower the elevator. The motor turns gear A with a constant angular acceleration, αA. The gears of the motor have the following radiuses: RA = 75 mm, RB = 200 mm, RD = 100 mm a) Determine the maximum angular acceleration of gear A, αAmax. b) Determine the tension in the cable, T, at this maximum acceleration.

PROBLEM #4 (20 points) Answers: A laboratory freight elevator, including its load, has a mass of 500 kg. It is prevented from rotating by the track and wheels mounted along its sides. The elevator is used to carry highly sensitive cquipment so it cannot execcd an acceleration of 3 m/s A geared motor is used with the cable/pulley system shown below to raise and lower the elevator. The motor turns gear A with a constant angular acceleration, α am have the following radiuses: R 75 The gears of the motor mm, RB 200 mm, RD a) Determine the maximum angular acceleration of gear A, aAmax. b) Determine the tension in the cable, T, at this maximum acceleration. 100 mnm

Answer 1

a) Obtain the velocity at point p as follows: V = v=x4 Obtain the acceleration at point p as follows: a, = ax 4 a, = 3x4 a, = 12 m/s? Obtain the acceleration at point D. a, = a= 12 m/s? Obtain the acceleration at point B. dg R; az _ 200 az = 2 m/s ag = 24 m/s?

Obtain the angular acceleration at B. dA 200 24 0x = 75 * (200x10^) (a :)= 320 rad/s? b) draw the free body diagram of the cord. T 21 T ma 500 x 9.81

calculate the tension in the cord. Applying force equilibrium equations as follows: 4T - mg = ma mg + ma 4 m(g+a) T= T = 500X (9.81+3) T =- T =1601.25 N