Problem 19-8 (No web address to a solutions manual please) The 50-kg cylinder ha
ID: 1817607 • Letter: P
Question
Problem 19-8 (No web address to a solutions manual please)
The 50-kg cylinder has an angular velocity of 30 rad/s when it is brought into contact with the horizontal surface at C. If the coefficient of kinetic friction is muc = 0.2, determine how long it will take for the cylinder to stop spinning. What force is developed in link AB during this time? The axle through the cylinder is connected to two symmetrical links. (Only AB is shown.) For the computation, neglect the weight of the links. (ans: FAB = 48.7 N, t = 1.64 s, N = 457.22 N) If the boxer hits the 75-kg punching bag with an impulse of I = 20 N middot s, determine the angular velocity of the bag immediately after it has been hit. Also, find theExplanation / Answer
4 forces on the cylinder: ( = 20o)
gravity mg, normal force N, applied force 2F (2 links), friction f = N
vertical net force = N + 2Fsin - mg = 0,
f/ + 2Fsin = mg
so 2F = (mg - f/)/sin
horizontal net force = 2Fcos + f = ma
f = mr - 2Fcos
f = mr - (mg - f/)cos/sin
ftan = mrtan - mg + f/
ftan = mrtan - mg + f
f = (mg - mrtan)/(1 - tan)
net torque = f*r = I* (I = mr2/2)
(mg - mrtan)/(1 - tan)*r = mr2/2
2(g - rtan)/(1 - tan) = r
2g - 2rtan = r - rtan
2g = r(1 + tan)
= 2g/[r(1 + tan)] = 18.29 rad/s2
t = / = 1.640 s
N = f/ = m(g - rtan)/(1 - tan) = 457.2 N
F = (mg - N)/(2sin) = 48.66 N