Find the value of x in the triangle.
2 answers:
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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
