Question

STAP 5.) A pulley is rotating at an angular velocity of 32 revolutions per minute. The radius of the pulley is 0.3 m. a.) How what is the angular distance the pulley rotates in 5 sec? b.) What is the linear distance the pulley rotates in 5 sec? c.) If a motor takes 30 sec to speed up the pulley to 82 revolutions per minute, what was the angular acceleration the motor applied? d.) How far will the pulley have traveled while accelerating?

Answer 1

1)

Force of friction, Fs = m*v^2/r

= 80*3^2/2

= 360 N

2)

a)

a) Torque = r1*F1*sin(theta)

= 0.25*80*sin(90)

= 20 N.m

b) Torque = r2*F2*sin(90)

F2 = Torque/r2

= 20/0.1

= 200 N

3) Torque = r*F*sin(theta)

= 1*50*sin(75)

= 48.3 N.m

4)

a) cenetripetal force = m*v^2/L

T = m*v^2/L

b) T = 5*2^2/2

= 10 N

5)

a) theta = w*t

= 32*(2*pi/60)*5

= 16.8 radaians

b) d = r*theta

= 0.3*16.8

= 5.04 m

c) alfa = (wf - wi)/t

= (82 - 32)*(2*pi/60)/30

= 0.174 rad/s^2

d) theta = wi*t + (1/2)*alfa*t^2

= 32*(2*pi/60)*30 + (1/2)*0.174*30^2

= 179 radians