Question

A cricket ball is rolled on ice with a velocity of $5.6\,{\rm{m/s}}$ and comes to rest
after traveling$8\,{\rm{m}}$. Find the coefficient of friction. Given $g =
9.8\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}$

Answer 1

Hint: This solution is solved by using second equation of motion ${v^2} = {u^2} + 2 \times a
\times s$, acceleration, and frictional force formula $f = \mu {\rm N}$.
Complete step by step answer:
When the ball comes to rest at $8\,{\rm{m}}$, from the second equation of motion,
${v^2} = {u^2} + 2 \times a \times s$
Put the final velocity value as $0$, and the distance as $8\,{\rm{m}}$.
To do this job successfully we get the value of the necessary acceleration as
$\begin{array}{c}{v^2} = {u^2} + 2as\\0 = {\left( {5.6} \right)^2} + 2 \times a \times 8\\16a = -
31.36\\a = - \dfrac{{31.36}}{{16}}\end{array}$
$a\; = - 1.96\dfrac{m}{{{s^2}}}$
Now we know the friction force is given by μN, where N is the usual reaction force exerted on
the ball by the surface and μ is the surface friction coefficient.
So, the acceleration generate by frictional force $ = \dfrac{{\mu {\rm N}}}{M}$.
Where, M is the mass of the ball.
Also, $N = Mg$
Where, g is the gravitational acceleration,
Thus, the acceleration generated $ = \mu g$
From the first expression, $\mu g = 1.96$
So,
$\begin{array}{c}\mu = \dfrac{{1.96}}{{9.8}}\\ = 0.2\end{array}$
Hence, the required answer is $0.2$.
Additional information:

Initial and final velocity: Initial velocity defines how rapidly an object moves when gravity
applies force on the body first. On the other hand, the final velocity is a vector quantity which
measures a moving body's speed and direction after its maximum acceleration has been reached.
Acceleration: Acceleration is the rate at which speed varies. Acceleration typically means
velocity is changing, but not always. As an object travels at a constant speed along a circular
path, it is still moving, since its velocity direction is changing.
Note: In this solution, first using second equation of motion for finding acceleration and then use
frictional force formula $f = \mu {\rm N}$, later put all the value and find the required answer.