Friction in Elastic collision?

Classical Mechanics Level 5

A small spherical ball undergoes an elastic collision with a rough horizontal surface. Before the collision, it is moving at an angle of $\theta$ with the horizontal. Assume that friction $f=\mu N$ during the contact period, where $N$ is the normal reaction and $\mu$ is the coefficient of friction.

Find the value of $\theta$ (in degrees) to the nearest integer such that the horizontal range of the ball after hitting the surface is maximized, given $\mu=\frac{\sqrt{3}}{2}$ .

The answer is 15.

1 solution

Rajdeep Brahma
Apr 22, 2017

Velocity along $Y$ direction is same in magnitude before and after the collision (elastic).

Let the normal reaction be $N$ .

Impulse = $N.t = 2mv (\sin \theta)$ .

Along $x$ axis, $I = f.t = \mu N.t = 2\mu m v.(\sin \theta)$ .

Using $dI=dP$ , we get, $v_x$ (velocity along $x$ after collision) = $v((\cos \theta)-2\mu \sin(\theta))$ .

Range= $\dfrac{2v(\sin \theta)}{g} \times v_x$

Maximize R to get $\cot( 2\theta) = 2\mu = \sqrt{3}$ .

So, $2x=30, x=\boxed{15^\circ}$ .

Did the same!!!

A Former Brilliant Member - 4 years ago

Try myne, a bit modified one

Partially Elastic

Md Zuhair - 3 years, 9 months ago

Will surely try!!!! Nice question BTW.

A Former Brilliant Member - 3 years, 9 months ago

@A Former Brilliant Member – Thanks bro

Md Zuhair - 3 years, 9 months ago

Friction in Elastic collision?

The answer is 15.

1 solution

0 pending reports