An automobile is sliding down an icy road which is inclined at a 15 degree angle

Question

An automobile is sliding down an icy road which is inclined at a 15 degree angle. The mass of the car is 1500 kg. Assume friction acts to slow the car

A) Fill in the table of x adn y components for al the forces. (answers in MKS units)

B) if the car is initially moving at 12 m/s when it begins to slide, determine the acceleration needed to stop the car over a displacement of 61 cm.

C) determine the required force of friction needed to produce teh acceleration in part c

D)Determine the normal force on the car.

Explanation / Answer

let mue is the coefficient of kintic friction

A) Fx = m*g*sin(theta) - mue*m*g*cos(theta)

   Fy = m*g*cos(theta)

B) v1 = 12 m/s, v2 = 0, s = 0.61 m

v2^2 - v1^2 = 2*a*s

a = (v2^2-v1^2)/(2*s)

= (0^2 - 12^2)/2*0.61

= -118 m/s^2

C) let Ff is the force of friction

Fnet = Ff - m*gsin(theta)

m*a = Ff - m*g*sin(theta)

Ff = m*g*sin(theta) + m*a

= 1500*9.8*sin(15) + 1500*(118)

= 180804 N

D)

Ff = N*cos(theta)

N = Ff/(cos(15))

= 187182 N

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