Answer:
Maximum amount of cargo(in lbs) = 1455 lbs
Explanation:
Assume the maximum amount of cargo is w ,
The breaking efficiency will be given by
- E = (80 - 0.01 w) %
Stopping distance is given by formula ,
Stopping distance = ![\frac{v^{2} }{2g(u - 0.01n)E}](https://tex.z-dn.net/?f=%5Cfrac%7Bv%5E%7B2%7D%20%7D%7B2g%28u%20-%200.01n%29E%7D)
where,
v (velocity), u (coefficient of road adhesion), n (grade)
Put E from equation 1
Stopping distance = ![\frac{v^{2} }{2g(u - 0.01n)(80 - 0.01w)0.01}](https://tex.z-dn.net/?f=%5Cfrac%7Bv%5E%7B2%7D%20%7D%7B2g%28u%20-%200.01n%29%2880%20-%200.01w%290.01%7D)
Stopping distance is given as 275 ft ,
V= 70 mi/hr = 70 x 1.4667 ft/s = 102.67 ft/s
Put all given values in above equation
275 = ![\frac{(102.67)^{2} }{2(32.18)(0.95 - 0.01(4))(80 - 0.01w)0.01}](https://tex.z-dn.net/?f=%5Cfrac%7B%28102.67%29%5E%7B2%7D%20%7D%7B2%2832.18%29%280.95%20-%200.01%284%29%29%2880%20-%200.01w%290.01%7D)
(80 - 0.01w ) = ![\frac{(102.67)^{2} }{2(32.18)(0.91)(0.01)(275)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28102.67%29%5E%7B2%7D%20%7D%7B2%2832.18%29%280.91%29%280.01%29%28275%29%7D)
( 80 - 0.01w ) = 65.45
0.01w = ( 80 - 65.45)
w = 14.55 x 100
w = 1455 lbs