Question

3)A mass of 4 kg rests on a horizontal plane. The plane is gradually inclined until at an angle 0=15° with the horizontal, the mass just begins to slide. What is the coefficient of static friction between the block and the surface?

Answer 1

Given:

Mass, m = 4 kg

ANgle of inclination,θ = 15°

Let's find the coefficient of static friction between the block and the surface.

To find the coefficient of static friction, apply the formula:

`\begin{gathered} \mu_sN=fs \\ \text{Where:} \\ N=mg\cos \theta \\ \\ f_s=mg\sin \theta \end{gathered}`

Thus, we have:

`\begin{gathered} \mu_smg\cos \theta=mg\sin \theta \\ \\ \mu_s=(mg\sin \theta)/(mg\cos \theta) \\ \\ \mu_s=tan\theta \end{gathered}`

Therefore, the coefficient of static friction will be:

`\begin{gathered} \mu_s=\tan (15) \\ \\ \mu_s=0.267\approx0.27 \end{gathered}`

Therefore, the coefficient of static friction between the blcok and the surface is 0.27

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