Modeling Friction Forces

Purpose: The purpose of the experiment was to utilize wooden blocks to see friction forces in action and to calculate the acceleration of the systems.

Procedure:
1) The first part of the experiment involved using a wooden block attached to a cup full of water with a string using a pulley system. The block was set on top of the table while the pulley was set at the edge. We let the cup full of water hang from the edge of the table by the string attached to the pulley system. This experiment was used to determine the coefficient of static friction between the block and the table. We measured it by adding water to the cup until the block just barely began to move. We did this for 1, 2, 3, and 4 blocks on top of each other. For some of these trials we had to use weights since the water in the was filled to the top and the blocks still would not move at all.

2) We then proceeded to use a Force Sensor to measure how much force did it take to pull the 1, 2, 3, 4 blocks respectively so that we could find the kinetic friction of the system respectively.

3) Afterwards we used height to calculate static friction. By using a ramp and ring stand with a clamp we were able to set the ramp at an angle. We adjusted the height so that the block would barely move and then used that to find out the static friction of the system. This was done to only one block.

4) Next, we measured the kinetic friction of the system by doing a similar experiment as the height one except this time adjust the height so that the block would slide down. We put a motion sensor on the bottom of the ramp to record just how fast it was going and then use it to find the kinetic friction of the system.

5) After that we used the same set up as the previous one but instead we reinserted the pulley into the system and put a weight at the end of the pulley so it could hang. This was used to predict the acceleration of the system so that we could put the friction forces we acquired to the test and see how close we were to the results. The motion sensor was also placed at the bottom so we can get an experimental value of acceleration.

Data:
1) We calculated for the force of static friction for the first runs of the 1, 2, 3, 4 blocks respectively and also the Normal Force and put the in this chart below.

The graph below shows the resultant coefficient of maximum static friction and as you can see, the second and third data points were a little off.

2) After using the force sensors we came to the this graph below and using the cleaner data of when the force looks like it is almost constant, we were able to find the kinetic friction force.

4) Below is the graph of the resulting kinetic friction force used when using the motion detector when letting the block slide down the steep ramp.

5) Below is the data table that the motion sensor acquired for the the acceleration of the system when using the block-weight pulley.

The graph below is the resulting acceleration of the system that we found experimentally.

Calculations:
1) The calculations below were from the first part of the experiment were we used the block-water pulley system to find the coefficient of static friction. The coefficient of static friction was 0.406

3) Below is the calculation that we used to find the static friction of the block at an incline when we were adjusting height. The value is 0.364.

4) The calculations below were from the fourth part of the experiment and it shows how we got the kinetic friction of the experiment when on a steep inclined ramp. The value of the coefficient of static friction is 0.355.

5) The calculations below show how we came to the acceleration of the system of the block-weight system. The theoretical value we got is 0.565 m/s^2 and the experimental value was 0.6483 m/s^2.

Summary: We started by using the block-water pulley system to find the coefficient of static friction between the block and the table and graphing the force of static friction with the normal force of the block  to find a relationship. The relationship was the coefficient of static friction. For the experimental value we got 0.3285 and for the calculated value we got 0.406 which is +23.6% off. This number is pretty big but the reason for it was because we did not put the exact amount of water for maximum static friction since it requires for the object to remain still and in order for us to calculate it we have to let the block slide a little. It was also very difficult to get the block still having it moved for a little bit. 

Then we used the force sensor to calculate the kinetic friction of the experiment using the force graph of the recorded data. After that we found the coefficient of static friction of the wooden block on top of an inclined ramp. Sine it was a different surface we got 0.364. Next, we used the acceleration found from the block sliding down a steep ramp with the motion sensor to calculate the coefficient of static friction for the ramp. We got 0.355. Finally we predicted the acceleration of the system by using the previous coefficient of static friction. Our theoretical value was 0.565 m/s^2 while our experimental value was 0.6483 m/s^2. The percent error of the theoretical value is -12.8%. The reason being is because we can not get perfect reading from the machine and we also started putting stuff away before we knew we had to do this part of the experiment. We may also have gotten a different block which affected the result. Overall though, this lab was successful in showing us how the different friction forces affect objects on different surfaces.