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 body of mass $2 kg$ is lying on a rough inclined plane of inclination $30 °$ . Find the magnitude of the horizontal force needed to move the block up the incline.(Coefficient of static friction $= 0.2$ , $g = 10 m s^{- 2}$ .)

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 $R$ acting between the surfaces, $f = μ R$ .

Let $μ$ be the coefficient of friction, $R$ be the normal reaction between block and the plane and $F$ be the force applied.

To move the block up the incline, the net force up the incline must be greater than or equal to the net downward force, down the incline.

$\Rightarrow F_{u p} \geq F_{d o w n}$

$\Rightarrow F \cos (30 °) \geq μ R + m g \sin (30 °) . . . (1)$

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

$R - m g \cos (30 °) - F \sin (30 °) = 0$

$\Rightarrow R = m g \frac{\sqrt{3}}{2} + \frac{F}{2}$ .

Substitute the values of $R$ and $μ$ in equation $2 kg$ , we get,

$\Rightarrow F \frac{\sqrt{3}}{2} \geq 0.2 \times (m g \frac{\sqrt{3}}{2} + \frac{F}{2}) + m g \frac{1}{2}$

$\Rightarrow F (\frac{\sqrt{3}}{2} - \frac{1}{10}) \geq m g (\frac{\sqrt{3}}{10} + \frac{1}{2})$

$\Rightarrow F \geq \frac{2 \times 9.8 \times (\frac{\sqrt{3}}{10} + \frac{1}{2})}{(\frac{\sqrt{3}}{2} - \frac{1}{10})} \approx 17.577$

$\Rightarrow F \geq 17.577$ .

With a minimum force of $17.577 N$ , the body will move up the incline with a constant velocity, as the net force acting on it is zero.

A body of mass $2 kg$ is lying on a rough inclined plane of inclination $30 °$ . Find the magnitude of the horizontal force needed to move the block up the incline.(Coefficient of static friction $= 0.2$ , $g = 10 m s^{- 2}$ .)

Important Questions on Friction

Learn and Prepare for any exam you want !

A body of mass 2 kg is lying on a rough inclined plane of inclination 30°. Find the magnitude of the horizontal force needed to move the block up the incline.(Coefficient of static friction=0.2, g=10 m s-2.)

Important Questions on Friction

Learn and Prepare for any exam you want !

A body of mass $2 kg$ is lying on a rough inclined plane of inclination $30 °$ . Find the magnitude of the horizontal force needed to move the block up the incline.(Coefficient of static friction $= 0.2$ , $g = 10 m s^{- 2}$ .)