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Sagot :
Answer:
0.335
Explanation:
We can make the following free body diagram
So, we can calculate the normal force as
Fn = mgcos(21.9)
Because the net force in the perpendicular axis is 0. Then, the friction force is equal to
Ff = μFn
Ff = μmgcos(21.9)
Where μ is the coefficient of friction.
Now, by the second law of newton, we have the following equation
Fnet = mgsin(21.9) - Ff = ma
Then
mgsin(21.9) - μmgcos(21.9) = ma
Now, we can solve the equation for μ, so
[tex]\begin{gathered} g\sin(21.9)-\mu g\cos(21.9)=a \\ \\ -\mu g\cos(21.9)=a-g\sin(21.9) \\ \\ \mu=\frac{a-g\sin(21.9)}{-g\cos(21.9)} \end{gathered}[/tex]So, replacing a = 2.48 m/s² and g = 10 m/s², we get:
[tex]\mu=\frac{2.48-10\sin(21.9)}{-10\cos(21.9)}=0.335[/tex]Therefore. the coefficient of friction is 0.335
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