Ch 18 problems

from numpy import *
dtr = pi/180
g = 9.81     # m/s2
gfps = 32.2  # ft/s2

hand written solution

hand written solution

M = 6e3  # N.m
mE,mC,md = 900,200,600   # kg
h,r,k = 5, 0.8, 0.6      # m
v = sqrt( 2*h*(M/r + g*(mC-mE))/( md*k**2/r**2 + mE + mC ))
print('speed is {:.3f} m/s'.format(v))

speed is 2.098 m/s

hand written solution

P = 200    # N
m = 15     # kg
l = 0.6    # m
w = sqrt( 3/(2*m*l)*( P-m*g/(2*sqrt(2)) ) )
print('angular speed is {:.3f} rad/s'.format(w))

angular speed is 4.966 rad/s

hand written solution

R,r = 10,0.5  # ft
v = sqrt( 10*gfps/7*(R+r)*(1-1/sqrt(2)) )
print('speed is {:.3f} ft/s'.format(v))

speed is 11.894 ft/s

hand written solution

m,md = 10,5    # kg
l,r = 3,0.5    # m
Qi,Qf = 60*dtr,30*dtr  # rad
DV = m*g*l*( sin(Qf) - sin(Qi) )
denom = 5/12*m*l**2 + 1/4*m*l**2*( 9*(sin(Qf))**2 + (cos(Qf))**2 ) + 6*md*l**2*(sin(Qf))**2
w = sqrt( -2*DV/ denom  )
print('angular velocity is {:.3f} rad/s'.format(w))

angular velocity is 1.118 rad/s

hand written solution

m = 15     # kg
l = 4      # m
r,z = 5,7  # m
Q = arccos((r**2-l**2-z**2)/(-2*l*z))
hf = l/2*cos(Q)
rG2 = (z-hf)**2 + (l/2*sin(Q))**2
w = sqrt( g*(l-2*hf)/( 1/12*l**2 + rG2 ))
v = z*w
print('speed of A is {:.3f} m/s'.format(v))

speed of A is 4.000 m/s

hand written solution

h,k,r = 4,0.75,1  # ft
v = sqrt( 2*gfps*h/(1+(k/r)**2))
print('speed is {:.3f} ft/s'.format(v))

speed is 12.840 ft/s

hand written solution

r = 0.2  # m
w = sqrt( 3/5*g/r*(2*sqrt(3)-3) )
print('angular velocity is {:.3f} rad/s'.format(w))

angular velocity is 3.696 rad/s

hand written solution

r,z,xi = 1,0.5,3  # ft
kG = 0.7          # ft
k = 1.2           # ln/ft
l0 = 0.5          # ft
W = 50            # lb
m = W/gfps
xf = xi - pi*r/2
li = sqrt(xi**2+z**2)
lf = xf-z
w = sqrt( -k/m*(lf**2 - li**2 -2*l0*(lf-li))/(kG**2+r**2) )
print('angular speed is {:.3f} rad/s'.format(w))

angular speed is 1.804 rad/s