contestada

Two objects, M = 15.3 ks and m = 8.29 kg are connected with an ideal string and suspended by a pulley (which rotates with no friction) in the shape of a uniform disk with radius R = 7.50 cm and mass Mp = 14.1 kg. The string causes the pulley to rotate without slipping. If the masses are started from rest and allowed to move 2.50 m: What is the final speed (m/s) of mass m? What is the final angular speed (rad/s) of the pulley? How long (s) did it take for the masses to move from rest to the final position? Part (a) can be done by two methods: Forces and torques and energy conservation.

Respuesta :

onyebuchinnaji

(a) The final speed of the mass is 1.4 rad/s or 3.5 m/s.

(b) The time taken for the masses to move from rest to final angular speed is 0.71 s.

Net force on the pulley

The acceleration of the disk is determine from the net force applied to he pulley as shown below;

∑F = ma

Mg - mg = Mpa

Mg - mg = Mp(ω²r)

(15.3 x 9.8) - (8.29 x 9.8) = 14.1 x 2.5 x ω²

68.698 = 35.25ω²

ω² = 68.698/35.25

ω² = 1.95

ω = √1.95

ω = 1.4 rad/s

Linear speed

v = ωr

v = 1.4 x 2.5

v = 3.5 m/s

Angular acceleration

α = a/r

α = v²/r²

α = (3.5)²/(2.5²)

α = 1.96 rad/s²

Time to reach final angular speed

ωf = ωi+ αt

1.4 = 1.96t

t = 1.4/1.96

t = 0.71 s

Learn more about net force on pulley system here: https://brainly.com/question/14217083

Otras preguntas