Coefficient of Friction Experiment Notes

Objectives

• Determine the static ($\mu<em>s$) and kinetic ($\mu</em>k$) coefficients of friction using an inclined plane.

• Determine $\mu<em>k$ and $\mu</em>s$ using a horizontal setup with a pulley and applied forces.

• Compare the values of $\mu<em>k$ and $\mu</em>s$ obtained by the two methods.

• Demonstrate that the coefficients are independent of the normal force and that \mus > \muk.

Theory

• Friction is a force resisting motion between two surfaces.

• The normal force ($F_N$) acts perpendicularly to the surface of contact.

  • For a horizontal surface: $F<em>N = F</em>g = mg$

• On an inclined plane with angle $\theta$: $F<em>N = F</em>g \cos \theta = mg \cos \theta$

Static and Kinetic Friction

• Static friction ($f<em>s$) occurs between surfaces not in motion: $f</em>s \le \mu_s N$

  • If the applied force is less than the maximum static friction, there is no motion.

  • If the applied force exceeds the maximum static friction, the object moves.

• Kinetic friction ($f<em>k$) occurs when surfaces are moving relative to each other: $f</em>k = \mu_k N$

  • $\mu_k$ is assumed to be constant at slow speeds.

Inclined Plane

• At the angle where the block just begins to slip ($\theta<em>s$):$\mu</em>s = \tan \theta_s$

• When the block slides down at constant velocity (angle $\theta<em>k$): $\mu</em>k = \tan \theta_k$

Horizontal Plane with Pulley

• For static friction ($M<em>1$ is the block mass, $M</em>2$ is the mass needed to start movement):$M<em>2 = \mu</em>s M_1$

• For kinetic friction ($M<em>2$ is the mass needed to maintain constant velocity): $M</em>2 = \mu<em>k M</em>1$

Experimental Procedure: Inclined Plane

• Incline the plane until the block slides on its own to determine static friction.

• Measure Y (height of block) and X (distance from pivot line).

• Repeat with added masses.

• Calculate $\mu<em>s = \frac{Y}{X} = tan \theta</em>s$ for each mass.

• Repeat the procedure to find the angle at which the block moves at constant speed after a slight push to determine kinetic friction.

• Calculate $\mu<em>k = \frac{Y}{X} = tan \theta</em>k$ for each mass.

Experimental Procedure: Horizontal Plane with Pulley

• Place the board horizontally with a pulley at the edge.

• Attach a string to the block, run it over the pulley, and attach a mass holder.

• Add mass to the holder until the block just moves (static friction) or moves at constant velocity (kinetic friction).

• Record $M<em>1$ (block mass) and $M</em>2$ (mass on holder).

• Calculate $\mu<em>s$ and $\mu</em>k$ using the equations $M<em>2 = \mu</em>s M<em>1$ and $M</em>2 = \mu<em>k M</em>1$ respectively.

• Perform a linear least squares fit of $M<em>2$ vs. $M</em>1$ to determine the slopes, which are equal to $\mu<em>s$ and $\mu</em>k$.

Inclined Plane Setup (Alternative Method)

• Set up the inclined plane.

• Attach a string to the block, over the pulley, and attach a weight hanger to the other end.

• Adjust the string to be parallel to the inclined plane.

• Add masses to the hanger until the block moves at a constant velocity after using the vibration part of the apparatus.

• Record the total hanging weight in the Data Table 5.

• Add different amounts of mass to the block for different values of Fg and repeat step 5.

• Empty all the mass out of the block before proceeding to the next step.

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