Question

Canton Avenue in Pittsburgh, PA is considered to be one of the steepest roads in the world with a grade of 37%.

Answer 1

Answer:

a)  a = 3.53 m/sec²

b ) As force in the sense of movement is bigger than Fr  (that is  m*g*sin21 > Fr ) the car will slide down.

c) β = 11⁰

Step-by-step explanation: We must start calculating the angle of the road.

37% means that inclination is such that for 100 m of horizontal distance we will be up the path a 37 m, then tan α = 0.37  and α = 21⁰

a) According to Newtons second law

∑ Fx  =  ma    ⇒   if only gravity is acting

m*g* sinα = ma     ⇒  1000 Kg*9.8 m/sec² *sin 21°  = 1000 Kg*a

9.8 * 0,36 = a      ⇒   a = 3.53 m/sec²

b) Fr  =  μ*Fn      

∑ Fy  = 0  

m*g*cos21° - Fn  =  0        Fn  =  1000*9.8*cos21°     Fn  = 9143.4 [N]

Then  Fr = 9143.4 * 0,3     ⇒  Fr = 2743.02 [N]

And  

m*g*sinα   = m*g*sin21⁰   =  1000* 9.8* 0.36  =  3528 [N]

As force in the sense of movement is bigger than Fr  (that is  m*g*sin21 > Fr ) the car will road down.

c) If μk  =  0.2

m*g*sinβ   = 9800* sinβ - 9143.4*0.2 = 0

sinβ  = 1828.68/9800     ⇒   sinβ  =  0.1866   ⇒ β = 11⁰