Answer:
0.114
Explanation:
There are two forces acting on the cart in the direction along the cart:
- The component of the gravitational force in the direction parallel to the ramp, [tex]mg sin \theta[/tex], down along the ramp
- The force of friction, [tex]\mu N[/tex], up along the ramp
So the equation of motion along this direction is:
[tex]mg sin \theta - \mu N = ma[/tex] (1)
where
m is the mass of the cart
[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity
[tex]\theta=10^{\circ}[/tex] is the angle of the ramp
[tex]\mu[/tex] is the coefficient of kinetic friction
N is the normal force exerted by the ramp on the cart
[tex]a=0.60 m/s^2[/tex] is the acceleration of the cart
The normal force can be found from the equation of the forces along the direction perpendicular to the ramp; in fact, the normal force is balanced by the component of the weight perpendicular to the ramp, so we have:
[tex]N-mg cos \theta = 0[/tex]
From which we get:
[tex]N=mg cos \theta[/tex]
Substituting into (1),
[tex]mg sin \theta - \mu mg cos \theta = ma[/tex]
And solving for [tex]\mu[/tex], we find the coefficient of friction:
[tex]\mu = \frac{g sin \theta - a}{g cos \theta}=\frac{(9.8)(sin10^{\circ})-0.60}{(9.8)(cos 10^{\circ}}=0.114[/tex]
