Answer to Question #122191 in Classical Mechanics for McLeod

Question

A car of mass 1 ton decelerates down an incline hill which makes an angle of 15⁰ to the valley below.
a)Find normal force
b)Calculate the frictional force acting on the mass.
c)What is the coefficient of the kinetic friction between the car and the road?
d)Calculate the cars deceleration.

Please show working out.
Thanks.

Answer 1

Here,question is ill framed and circular as if car is decelerating, there should be provided Kinetic Frictional force or kinetic frictional coefficient (none is given).

So, I assumed kinetic frictional force is $f_R$ .

Let's draw the free body diagram.

Given, $M=1000kg$ ,$\alpha=15^{\circ}$ , let $g=10m/s^2$

a). from the FBD,

$$N=Mg\cos(\alpha)\implies N=9659.25\:Newton$$

b).Let, $\mu$(static) is the frictional coefficient and since $\mu=\tan(\alpha)$ ,thus $\mu=0.2679$

$$f=\mu N\implies f=2588.18N$$

c).

$$\mu_k=\frac{f_k}{N}=\frac{f_R}{N}\\ \implies \mu_k=\frac{f_R}{9659.25}=10^{-4}f_R$$

d).

Let, declaration be $a$ thus,

$$a=\frac{Mg\sin(15^{\circ})-f_R}{M}$$