Question

A coin is pushed down tangentially from an angular position $\theta$ on a cylindrical surface, with a velocity v as shown in the figure. If the coefficient of friction between the coin and surface is $\mu$, find the tangential acceleration of the coin.

• A. g(sin - cos )
• B.
• C.
• D.

Answer 1

The correct option is D

As the coin slides down, friction is kinetic and acts up along the plane.

Equation of motion : $\sum F_r=N-mgcos\theta =m{a}_r$ ........... (i)

$\sum F_t=mgsin\theta -f_k=m{a}_t$ ........... (ii)

But $f_k=\mu N$ ........... (iii)

And centripetal acceleration is $a_r$ = $\frac{m{v}^2}{R}$ ........... (iv)

Substituting $f_k$ from equation (iii), in equation (ii),

We get $a_t=gsin\theta -\frac{\mu N}{m}$ ...........(v)

Now, substituting N from equation (i) in equation (v), we get $a_t=g(sin\theta -\mu cos\theta )-\frac{\mu v^2}{R}$