First slide

Work

Question

A block starts moving up an inclined plane of inclination $30^{0}$ with an initial velocity of $v_{0}$ . It comes back to its initial position with velocity $\frac{v_{0}}{2}$ . The value of the coefficient of kinetic friction between the block and the inclined plane is close to $\frac{I}{1000}$ . The nearest integer to I is ___

Moderate

Solution

$\begin{array}{l} Work done by all fores = Δ K . E \\ I n u p w a r d j o u r n e y, \\ - mgh - μ mg (h) \sqrt{3} = - \frac{1}{2} {mv}_{0}^{2} \\ I n d o w n w a r d j o u r n e y, \\ mgh - μ mg (\sqrt{3} h) = \frac{1}{2} m {(\frac{v_{0}}{2})}^{2} \\ Dividing equations \frac{1 + \sqrt{3} μ}{1 - \sqrt{3} μ} = 4 \\ \Rightarrow μ = \frac{\sqrt{3}}{5} \\ \Rightarrow μ = \frac{346}{1000} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App