March 16/ March 18 Modeling Friction Forces

Objective: Five mini experiments are included in this modeling friction force lab. The five experiments examine different aspects of friction using different apparatuses.

Part 1: Static Friction
The Set-Up:

A wooden block sits on the surface of the metal track. The block is connected by a string to an empty Styrofoam cup. Both the cup and the block are not moving because the frictional force is greater than the tension force from the cup. The metal track is placed so that the cup is hanging in the air. In this way, the notable forces that acting on the cup would be tension from the string and the weight of the cup and water. We fill the cup with a little water at a time until the block begins to slide. Once the block slides, we weight the mass of the water. We also record the mass of the block.

Next, repeat this process with more blocks. We use four blocks in total, and we record the mass of the water and the mass of the blocks.

Data Collection:

The following is a table showing the mass of the block(s) and the mass of cup and water

Number of blocks	Mass of the block(s) in kg	Mass of cup and water in kg
1 block	0.1307	0.0321
2 blocks	0.2557	0.0429
3 blocks	0.3800	0.0852
4 blocks	0.6179	0.1037

Here is another table showing the normal force and frictional force of this set up. The normal force is the weight of the block(s). The maximum static friction force is the weight of the cup and water.

Number of blocks	Normal Force (N)	Friction Force (N)
1	1.28	0.31
2	2.51	0.42
3	3.72	0.84
4	6.06	1.02

Normal Force vs Friction Force Graph

Here is a graph taking normal force as x-axis and maximum static friction force as y-axis. The slope of the graph is the static friction between the block and the surface of the metal track. The value we obtain is µs= 0.23.

This is a calculation assuming the ideal situation. It also shows the calculation to get the coefficient of static friction, µs, between the block and the table. Here, the µs =0.24, compares to µs=0.23 using loggerpro.

Part 2: Kinetic Friction

The Set-Up:

We examine the kinetic friction by pulling a wooden block using a force senor. The wooden block has a red felt on its bottom and it is connected to a string. The other side of the string is connected to a force sensor. The data are recorded using loggerpro. A person pulls the block through the force sensor horizontally; the block is moves at a constant speed.  Then we can find the average force on loggerpro. In the same way, we repeat the process using two blocks, then three, until we get to four.

Data Collection:

Forces and time graph. These are the four trails records by loggerpro

The force values we get are:

Number of block(s)	The Pulling Force (N)
1	0.3415
2	0.6301
3	0.8197
4	1.196

The force and time graph for one block (first trial)

According to the graph, the average force for one block is 0.3415 N. The weight of the block(s) is the same as in part 1. We use the formula

F _pull = µ_k N

This is the table of normal force from part 1, we use the same blocks and the same order in this second experiment.

Number of blocks	Normal Force (N)
1	1.28
2	2.51
3	3.72
4	6.06

The force 0.3415 newton is the force for 1 block.

F pull = µk N

0.3415= µk (1.28)

µk=0.27

Please note that normally, the coefficient of static friction is greater than the coefficient of kinetic friction. Here we have µk= 0.27 and µs is 0.24 from the last experiment.

Part 3: Static Friction from a Sloped Surface

The Set-Up:

In this experiment, one block and an angle measurement device is place on the metal track. We tilt one end of the track until the block begins to move. Our goal here is to get the angle so that we can calculate the coefficient of static friction between the block and the metal track.

Data Collection:

The angle we get is 14 degree. 

We use Newton’s Second Law, F= ma, to calculate the coefficient of static friction. The coefficient of static friction is 0.24, just like part 1!

Part 4: Kinetic Friction from Sliding a Block Down and Incline

The Set-Up:

Here the metal track is tilted to a certain angle. The motion sensor is mounted on the higher end of the metal track. A block is to be let go a short distance away from the motion sensor. The block would accelerate downward. We use loggerpro to record the acceleration data. We want to find the coefficient of kinetic friction between the block and the surface of the metal track.

Data Collection:

The mass of the block is 0.1341 kg.

The incline is 25.4 degree.

Time vs Velocity graph, the slope is the acceleration

According to loggerpro, the acceleration of the block is 1.854 m/s^2.

Here is the calculation using F= ma.

The coefficient of kinetic friction of the metal track and the block is 0.266.

Part 5: Predicting the Acceleration of A Two Mass System

The Set-Up: 

The block is on the metal track, a string attachment the block to a weight. The weight is hanging freely in the air. The motion sensor is on the other side of the block to record the acceleration of the block as the weight falls.

Data Collection:

The goal of this experiment is to derive the acceleration of the block using the coefficient of kinetic friction we get from last experiment, µk=0.266. Then we check with loggerpro to see how accurate we are. 

From the calculation, we get an acceleration equals to 0.836 m/s².

Here is what the loggerpro records.

Velocity vs Time graph. The slope is the acceleration.

The loggerpro estimates that the acceleration is 0.5571 m/s².

It is different from our calculation result because loggerpro records the actual experiment instead of the ideal situation we assume in our calculation. During the experiment, some things that could affect the acceleration of the block may be the uneven surface of the metal track, human technique and air resistance