Question

A car has a mass of 1500 kg. If the driver applies the brakes while on a gravel road, the maximum friction force that the tires can provide without skidding is about 7000 N. how long are the skid marks

Answer 1

Explanation:

Given data:

mass of the car = 1500 kg

maximum friction force = 7000 N

initial velocity v_i = 20 m/s ( it is not given in the question just an assumption)

final velocity v_f = 0 m/s

$\begin{array}{l}

\sum F_{y}=M g-F_{n}=0 \\

\sum F_{x}=-F_{s}=m a_{x} \\

-F_{s}=m a_{x}

\end{array}$  

$a_{x}=\frac{-F_{s}}{m}=\frac{-7000}{1500}$

$a_{x}=-4.7 \mathrm{~m} / \mathrm{s}^{2}$

Now we can find the distance from this formula:

$v_{f x}^{2}=v_{i x}^{2}+2 a_{x}(\Delta x)$

$0=20^{2}+(2 \times-4.7 \times \Delta x)$

$20^{2}=9.4 \Delta x$

$\Delta x=\frac{20^{2}}{9.4}=42.55 \mathrm{~m}$

So, the shortest distance in which the car can stop safely without kidding

=42.55 m