Respuesta :
Answer:
The coefficient of kinetic friction is 0.382.
Explanation:
Given:
Angle of inclination is, [tex]\theta=20.0[/tex]°
Mass of package is, [tex]m=2.50\ kg[/tex]
Initial speed of package is, [tex]u=2.00\ m/s[/tex]
Final speed of the package at the bottom is, [tex]v=0\ m/s[/tex]
Distance of travel along the incline is, [tex]d=12.0\ m[/tex]
Acceleration due to gravity is, [tex]g=9.8\ m/s^2[/tex]
Let the coefficient of kinetic friction be [tex]\mu[/tex].
Now, the frictional force will be acting along the incline but in the direction opposite to the direction of motion.
So, the net acceleration acting on the package will be up the incline and is equal to:
[tex]a=\mu g\cos\theta-g\sin\theta[/tex] ----------------- 1
Now, using equation of motion, we have:
[tex]v^2-u^2=2ad\\\\0-(2.00)^2=2a(12.0)[/tex]
Solving for 'a', we get:
[tex]-4.00=24.0a\\\\a=-\frac{4}{24}=-\frac{1}{6}\ m/s^2[/tex]
Now, plug in the value of 'a' in equation (1). This gives,
[tex]\mu g\cos\theta-g\sin\theta=\frac{1}{6}[/tex] ( Neglecting negative sign)
Plug in all the given values and solve for [tex]\mu[/tex]. This gives,
[tex]9.8(-sin(20)+\mu cos(20))=\frac{1}{6}\\\\-0.342+\mu\times 0.94=0.017\\\\0.94\mu=0.342+0.017\\\\0.94\mu=0.359\\\\\mu=\frac{0.359}{0.94}=0.382[/tex]
Therefore, the coefficient of kinetic friction is 0.382.
The coefficient of kinetic friction is 0.346
The mass of the package is m = 2.5kg
The angle of the incline θ = 20°
Initial speed u = 2 m/s
and the distance traveled is d = 12 m,
Kinetic Friction:
The kinetic friction acts opposite to the motion of the body and is given by:
[tex]f=\mu_kmgcos\theta[/tex]
where [tex]\mu_k[/tex] is the coefficient of kinetic friction.
The equation of motion of the package down the inclined plane is given by:
[tex]mgsin\theta-\mu_kmgcos\theta=ma\\\\gsin\theta-\mu_kgcos\theta=a[/tex]
from the third equation of motion:
[tex]v^2-u^2=2ad\\\\0-2^2=2a\times12\\\\a=-\frac{1}{6}m/s^2[/tex]
so,
[tex]gsin\theta-\mu_kgcos\theta=a\\\\\mu_k=\frac{gsin\theta-a}{gcos\theta}\\\\\mu_k=\frac{9.8sin20-1/6}{9.8cos20}\\\\\mu_k=0.346[/tex]
Learn more about kinetic friction:
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