A 13.0 kg box is released on a 33 degree incline and accelerates down the incline at 0.20 m/s^2.
1. Find the friction force impeding its notion?
2. What is the coefficient of kinetic friction?
*Are we dealing with Kinetic or Static Friction...this will effect coefficient correct?
*The equation coefficient*m*g*cos angle DOES NOT give you the friction force
Wb = m*g = 13kg * 9.8N/kg = 127.4 N. =
Wt. of box.
Fb = 127.4N @ 33 Deg. = Foce of box.
Fp = 127.4*sin33 = 69.4 N. = Force parallel to incline.
Fv = 127.4*cos33 = 106.8 N. = Force perpendicular to incline.
1. Fn = Fp - Fk = ma
69.4 - Fk = 13 * 0.20 = 2.6
-Fk = 2.6 -69.4 = -72
Fk = 72 N = Force of kinetic friction.
2. u*Fv = Fk
127.4u = 72
u = 72 / 127.4 = 0.565 = Coefficient of
kinetic friction.
Correction:
-Fk = 2.6 - 69.4 = -66.8Fk = 66.8 N.
2. u*Fv = Fk
127.4u = 66.8
u = 66.8 / 127.4 = 0.524 = uk.
OOPs!
2. u*Fv = Fk
1o6.8u = 66.8
u = 66.8 / 106.8 = 0.625.
NOTE: Fv = 106.8 N.
To find the friction force impeding the motion of the box, we can use the equation:
F_friction = m * a
where F_friction is the friction force, m is the mass of the box, and a is the acceleration of the box down the incline.
1. Find the friction force impeding its motion:
Since the box is accelerating down the incline, the friction force is acting in the opposite direction. Therefore, the friction force is given by:
F_friction = m * a = (13.0 kg) * (-0.20 m/s^2)
Note that the negative sign is used to indicate that the friction force is opposite to the direction of motion. Calculate the multiplication to find the magnitude of the friction force.
2. To find the coefficient of kinetic friction, we need to use the equation:
F_friction = μ_kinetic * N
where F_friction is the friction force, μ_kinetic is the coefficient of kinetic friction, and N is the normal force.
The normal force is given by:
N = m * g * cos(angle)
where m is the mass of the box, g is the acceleration due to gravity, and angle is the incline angle. In this case, the angle is 33 degrees.
Once we have the normal force, we can substitute it into the equation to find the coefficient of kinetic friction:
F_friction = μ_kinetic * N
Now, use the previously calculated magnitude of the friction force and the normal force equation to solve for the coefficient of kinetic friction, μ_kinetic.