Answer to Question #306699 in Mechanics | Relativity for ED Angelo

Question

A car of mass 8000kg moves in a circular path of radius 100m with a linear velocity of 50m/s.Calculate the i) Angular velocity ii) Angle the tyre makes with the ground iii) condition for skidding for u(coefficient of friction)= 0.5?

Answer 1

Explanations & Calculations

a)

$\qquad\qquad \begin{aligned} \small \omega&=\small \frac{v^2}{r}\\ &=\small \frac{(50\,ms^{-1})^2}{100\,m}\\ &=\small 25\,rads^{-1} \end{aligned}$

b)

$\qquad\qquad \begin{aligned} \small R\cos\theta&=\small \frac{mv^2}{r}\\ \small R\sin\theta&=\small mg\\ \small \tan\theta&=\small \frac{rg}{v^2}\\ \small \theta&=\small \tan^{-1}\Big[\frac{100\times9.8}{50^2} \Big] \end{aligned}$ You can try getting the answer

c) The maximum possible speeding without skidding is when the maximum friction from the ground is possible. Apply F=ma towards the centre.

$\qquad\qquad \begin{aligned} \small F_{max}&=\small ma_{max}\\ \small \mu R&=\small m\frac{v_{max}^2}{r}\\ \small \mu mg&=\small \frac{mv_{max}^2}{r}\\ \small v_{max}&=\small \sqrt{\mu gr}\\ &=\small \sqrt{0.5\times9.8\times100} \end{aligned}$ Give it a try.