In order to determine the coefficients of friction between rubber and various surfaces, a student uses a rubber eraser and an incline. In one experiment, the eraser begins to slip down the incline when the angle of inclination is 36.4° and then moves down the incline with constant speed when the angle is reduced to 29.9°. From these data, determine the coefficients of static and kinetic friction for this experiment.
Any help would be great, thanks for your time!
So static: 0.73 and kinetic: 0.57, thanks!
Static friction is the friction acting on a body when the body is not in motion, but when a force is acting on it. Static friction is the same as the force being applied (because the body isn't moving). Static friction acts because the body tends to move when a force is applied on it.
Limiting friction is the friction on a body just before it starts moving. Generally, limiting friction is highest.
To determine the coefficients of friction in this experiment, we will use the concept of force equilibrium.
Let's start by understanding the forces acting on the eraser when it is about to slip down the incline at an angle of 36.4°:
1. The weight of the eraser acts vertically downward. We can decompose this force into its components:
- The force acting parallel to the incline, also known as the component of weight down the incline (Wx).
- The force acting perpendicular to the incline, also known as the component of weight perpendicular to the incline (Wy).
2. The normal force acts perpendicular to the incline and counteracts the force pushing the eraser into the incline.
3. The static friction force (Fs) acts parallel to the incline and opposes the force tending to make the eraser slide.
When the eraser is about to slip, the static friction is at its maximum before it starts decreasing. At this point, the static friction force is equal in magnitude and opposite in direction to the component of weight down the incline (Wx).
Now let's move on to the forces acting on the eraser when it is moving down the incline with constant speed at an angle of 29.9°:
1. The weight of the eraser continues to act vertically downward.
2. The normal force still acts perpendicular to the incline.
3. The kinetic friction force (Fk) acts in the opposite direction to the motion and has a magnitude equal to the force required to maintain constant speed.
The angle of inclination affects the weight component down the incline (Wx) and the normal force (Wy), which in turn affects the friction forces.
To determine the coefficients of friction, we can set up the following equations:
For the maximum static friction when the eraser is about to slip:
Fs = Wx
For the kinetic friction when the eraser is moving at constant speed:
Fk = Wx
To find Wx and Wy, we can use trigonometry:
Wx = mg * sin(θ)
Wy = mg * cos(θ)
Where m is the mass of the eraser and g is the acceleration due to gravity.
By measuring the angle of inclination and the masses involved and plugging the values into these equations, you can determine the coefficients of static and kinetic friction.
When there is no acceleration, the friction force (M g cosA *mu) equals the component of the weight in the direction down and parallel to the incline (M g sin A).
Therefore mu = sin A/cos A = tan A
Apply that equation both at the maximum ramp angle before slipping (in which case mu is the static friction coefficient) and the ramp angle that results in constant velocity (in which case mu is the kinetic friction coefficient).