Mar 16, 2015; Lab 7: Modeling Friction Forces

Purpose:

We want to measure the experimental both the kinetic and static coefficient of frictions, make predictions on acceleration, and compare the experimental to the predicted acceleration value.

Experiment:

Part 1:Static Friction
To measure coefficient of static friction, we use several wooden blocks and a cup of water as a system. The continuation of adding water into the cup eventually accelerates the system and at that point we can measure μ-static.

The masses are also measured before each trial

The following is our data table. We treat the weight of water (m-water*g) as static friction since that is the maximum amount of force needed to outrun the coefficient of static friction. 

Since f-static is lesser than or equal to N*μ-static, graphing N and f-static gives μ-static as a slope:

μ-static=.2829; proportional fit

Part 2:Kinetic Friction

In this part, we assume a constant velocity while pulling block(s) with string attach to force sensor. The force sensor is initially calibrated to recognize the sensitivity in mass.The sensor, therefore, record the data of 4 distinct trials shown below. We are only interested in the mean of each pull. Thus, we use this value as f-kinetic to find μ-kinetic of the system.

Since f-kinetic= μ-kinetic* N, and we keep our N the same as part 1, μ-kinetic is the slope of f-kinetic and N graph.

4 means of forces are collected from here for the graph below

N values remain the same. Proportional fit.

Therefore, coefficient of static friction for the lab table= .2829, μ-kinetic= .2482

Part 3: Static friction form a sloped surface

By measuring just an angle of when the block starts to accelerate, we can find μ-static.

This block takes more than 13° incline to start sliding

We approach this problem by first drawing FBD and solve for μ-static. As it turns out, everything cancels except for the angle that's needed for calculation.

Therefore, μ-static of the metal track= 0.325

Part 4: Kinetic friction from sliding block down incline

We need a motion sensor for this part to measure the acceleration of a block. Knowing that it takes 18° to overcome static coefficient, we increase the incline to 22.3° so that the system moves. The graph below is a screenshot of our data: a= 0.3230m/sec^2 (as a slope of velocity graph).

With given mass-block, angle, and acceleration, we can calculate μ-kinetic as the following:

a= 0.3230 m/sec^2

μ-kinetic= .3745

Part 5: Predicting "a" of 2-mass system

With a heavy enough hanging mass, the system will accelerate. This part also requires a motion sensor to collect the data of acceleration. We also use μ-kinetic= .3745 from the last part.

The block moves away from the sensor as the system accelerates.

acceleration= slope of velocity graph= 1.444m/sec^2

We predict the minimum hanging mass needed to accelerate the system and it's .047kg. So we decided to use a hanging mass of .074kg. On the right side, we derive an expression for acceleration and plug in previously measured values to find acceleration.

Error= -8.67%

Conclusion:

From this lab, we've noticed that μ-static > μ-kinetic, in most cases. The coefficient of friction (static and kinetic) depends only on the surface texture, not the area of contact nor mass of the block. Possible errors such as the one in part 5 can be from the fact that μ-kinetic of the metal track is larger compared to its μ-static, which means there are propagated errors in μ-kinetic.