Answer to Question #248950 in Mechanical Engineering for mazon47

Question

A vehicle has a wheel base of 3 m with a centre of gravity 0.8 m above ground level and 1.8 m in front of the rear axle. The coefficient of friction between the wheels and the road is 0.5. The vehicle is traveling horizontally at 90 km/h. Calculate the shortest distance at which the vehicle can be brought to a standstill by means of: 1.1. The brakes on the rear wheels only (14)

1.2. The brakes on both front and rear wheels. 

Answer 1

L = 3 m ; x = 0.8 m ; h = 1.8 m ;

μ = 0.5

Let   a = Maximum deceleration of the car,

m = Mass of the car,

FA and FB = Braking forces at the front and rear wheels respectively, and

RA and RB = Normal reactions at the front and rear wheels respectively.

rakes on the rear wheels only:

We know that when the brakes are applied to all four wheels and the vehicle moves on a level road, then

$R _B=m⋅g( \frac{L−μ⋅h−x}{L}) = m⋅9.81( \frac{3−0.5⋅1.8−0.8}{3}) = 4.28m$

$F_{ A }+F_{ B }=m .a$

$2μ.R _B=m⋅a$

$2×0.5×4.28m=m.a$

$a =4.28 \frac{m}{s^2}$