Name: Friction on a Single Block
Uploaded: 2019-07-19
Duration: 3 min 19 s
Description: Why is it hard to move a heavy bookcase across a carpeted floor? What is the reason behind it? Let's find out in this interesting video. Have fun learning!

Question

A block slides down an inclined surface of inclination

30 °

with the horizontal. Starting from rest, it covers

8 m

in the first two seconds. Find the coefficient of kinetic friction between the two.

Accepted Answer

Friction always acts opposite to the relative velocity between the two surfaces. And its magnitude is given by coefficient of friction $μ$ times the normal $N$ acting between the surfaces, $f = μ N$ .

Let $μ$ be the coefficient of friction and $N$ be the normal reaction between block and the plane.

Since, there is no acceleration in the direction of perpendicular to the incline, the net force will also be zero.

$N - m g \cos (30 °) = 0$

$\Rightarrow N = m g \frac{\sqrt{3}}{2}$

Using Newton's second law of motion,

$F_{n e t} = m a$

$\Rightarrow m g \sin (30 °) - μ N = m a$

$\Rightarrow \frac{m g}{2} - \frac{\sqrt{3} μ m g}{2} = m a$

$\Rightarrow a = \frac{g (1 - \sqrt{3} μ)}{2} = 5 (1 - \sqrt{3} μ)$ ... $(1)$

According to the question, the block travels a distance $s = 8 m$ in time $t = 2 s$ , and initial velocity $u = 0 m s^{- 1}$ .

Using second equation of motion,

$s = u t + \frac{1}{2} a t^{2}$

$\Rightarrow 8 = \frac{1}{2} \times a \times 2^{2}$

$\Rightarrow a = 4 m s^{- 2}$ ... $(2)$

Equating equations $(1)$ and $(2)$ , we get,

$\Rightarrow 5 (1 - \sqrt{3} μ) = 4$

$\Rightarrow μ = \frac{(1 - \frac{4}{5})}{\sqrt{3}} = \frac{1}{5 \sqrt{3}} \approx 0.115$ .

A block slides down an inclined surface of inclination $30 °$ with the horizontal. Starting from rest, it covers $8 m$ in the first two seconds. Find the coefficient of kinetic friction between the two.

Important Questions on Friction

Learn and Prepare for any exam you want !

A block slides down an inclined surface of inclination 30° with the horizontal. Starting from rest, it covers 8 m in the first two seconds. Find the coefficient of kinetic friction between the two.

Important Questions on Friction

Learn and Prepare for any exam you want !

A block slides down an inclined surface of inclination $30 °$ with the horizontal. Starting from rest, it covers $8 m$ in the first two seconds. Find the coefficient of kinetic friction between the two.