3/18/15: Modeling Friction Forces Lab 7

Purpose: To apply Newton's laws throughout five different experiments in order to determine the coefficients of kinetic and static friction.

Part 1 Static Friction:

We will be determining the coefficient of static friction using a pulley, wooden block, and cup. Below is an image of how to set up the experiment.

A wooden block with the felt-side placed on the table and a string attached to the block. A cup is attached to the string which hangs over the table by a pulley.

The procedure goes as follows:

1. Weigh a wooden block and record the mass. The system should be at rest before beginning. 
2. Carefully add water to the cup until the block begins to move. Record the mass of the cup.
3. Record the mass of another wooden block and place it on top of the existing block. Record the total mass of the blocks.
4. Carefully add water again to cup just until the blocks move. Record the mass of the cup with water.
5. Repeat this process until you have four blocks stacked on top of one another
6. By the end, a total of four different values of mass for the blocks and four different values of mass for the cups with water should be recorded.

Below is the collected data and free body diagram of the set up

We will input this data in to logger pro to determine the maximum coefficient of static friction.

Below is a data table consisting of our values input into logger pro

The force of friction should equal M Water + cup, which is the mass of the cup with water. We made sure to convert grams to kilograms. 

To determine the coefficient of static friction we plotted a friction force (N) vs. normal force (N) graph. The slope of the graph is our coefficient which was 0.3093.

Part 2 Kinetic Friction:

We will be measuring the coefficient of kinetic friction using a force sensor, wooden blocks, and string. Before beginning we made sure to calibrate the sensor with using a 500 g hanging mass. Using the same wooden blocks as before, we pulled the block across the table at constant speed, recorded the data in logger pro, and repeated this process until we generated four different graphs. By pulling the blocks at constant speed, the force of kinetic friction will equal the force of the pull. 

Once all four graphs have been created in logger pro, we determined the mean force exerted on each stack of blocks and generated another graph to find the coefficient of kinetic friction.

The mean value is the force exerted on each block. These values were the graphed and the slope of the graph represented to coefficient of kinetic friction. 

Friction (N) vs. Normal Force (N)

Our value was 0.2531. This makes sense seeing that the coefficient of kinetic friction should be smaller than the coefficient of static friction.

Part 3 Static Friction From A Sloped Surface: 

Again we will be measuring the coefficient of static friction, but this time using only a track and wooden block. We began by placing the block on a horizontal track, slowly raising one end of the track until the block started to slip. We then measured and recorded the angle the track made with the horizontal.

 

We were able to determine the coefficient of static friction by drawing a free body diagram and summing up the forces in the x and y direction. The force of static friction is equal to mgsinø because there is no acceleration in the x direction. We figured out µs is simply equal to tanø. 


Part 4 Kinetic Friction From Sliding A Block Down an Incline:

We will now be measuring the coefficient of kinetic friction. We set up a motion detecter at the top of a horizontal track steep enough so that a block will accelerate down the incline. We measured the angle of the incline and used a velocity vs. time graph to find the acceleration of the block. With this information we can use a free body diagram to again find µk. 

Set up of experiment

We used logger pro to collect a position vs time and velocity vs time graph. The slope of the velocity vs time graph is the acceleration of the block.

A free body diagram drawing of the set up and sum of all the forces leading to µk.

Part 5 Prediction the Acceleration of a Two-Mass System:

This last experiment we will take our coefficient of static friction and use it to derive an expression for what the acceleration of the block would be if we used a hanging mass heavy enough to accelerate the system. The set up used is a track, motion sensor, hanging mass, wooden block, pulley, and string. 

Below is a free body diagram and an equation we derived for the acceleration of our system. Based on µk we determined the acceleration to be 2.675 m/s^2.

We next used logger pro to generate a velocity vs. time graph and found the slope from the graph to be 1.137 m/s^2. Our values did not quite match.

Conclusion:

For this experiment, we determined µs and µk for various situations. We saw how pulling a mass at constant speed leads to µk being equal to the force our pull generated. We learned how to calculate µs from something as simple as raising a track and recording the angle it made with the horizontal when the block slipped. To tie it up, we used our value for µk to predict the acceleration of a system.