Lab Assignment 4: Frictional Forces

Instructor’s Overview

In many physics problems involving Newton’s laws of motion, you’ll see statements like, “assume a frictionless surface” or “neglecting air resistance…” In this lab we will be exploring both friction and air resistance, two resistive forces that are critical in the design of real-world products and systems. Understanding the effects of these types of forces is essential in the design of such things as aircraft, automobiles, braking systems, and countless other objects.

This activity is based on Lab 7 of the eScience Lab kit. Although you should read all of the content in Lab 7, we will be performing a targeted subset of the eScience experiments.

Our lab consists of two main components. These components are described in detail in the eScience manual. Here is a quick overview:

• • In the first part of the lab, you will measure the force it takes to pull objects of different mass. This experiment focuses on the effects of frictional forces. (eScience Experiment 1)
• • In the second part of the lab, you will investigate the effects of air resistance by performing controlled drops of coffee filters.

Notes:

• o Please follow the instructions in this document for the air resistance experiment.
• o Record all of your data in the tables that are provided in this document.

Take detailed notes as you perform the experiment and fill out the sections below. This document serves as your lab report. Please include detailed descriptions of your experimental methods and observations.

Abstract

Experiment 1 – Friction Between Surfaces.

Experiment Tips and Procedures:

Theory: Friction is the force caused by the contact of surfaces such as a cup of water on a table or by a fluid moving against a structure such as the wind blowing against a windmill.

The amount of force in the friction between a cup of water and the table depends on how much force is compressing the cup and table together. Thinking of Newton’s 3^rd law we recall that the weight of the cup pushes down on the table and the table pushes equally on the cup. We use the force of table pushing up on the cup and call this the normal force, normal because the vector angle is 90 degrees to the surface of the table.

It some cases it would not be correct to just use the weight of the object on the table. For example, we might be lifting up on that object and this lift counters some of the weight. If the object weighed 10 N and we applied a lift of 4 N the net force down would be 6N and this is also the normal force. The normal force is always equal to the NET force applied to the table.

Friction is always parallel to the surfaces, in the opposite direction that a sideways force is applied to make the object move. So if you pull the cup of water to the right the friction works against you and is a force to the left.

The force of friction is related to the normal force. The greater the normal force the greater the compression between the surfaces and the greater the force of friction. We measure the force of friction, label it Fr, and compare it to the Normal force, labeled Fn. The ratio of the Fr to Fn is called μ (the Greek letter mu). Once we know u we can use that to determine the force of friction once we know the normal force. This ratio, μ, is called the coefficient of friction.

When the object being studied is not moving we have a STATIC situation and the coefficient is labeled μ_s. When the object is moving we have a KINETIC situation and the coefficient of friction will have different value, we label it μ_k.

In general, μ =

Procedure:

1. Calibrate your spring scale. Holding it vertically adjust it to read 0.

2. Weigh the cups, you can put a small in the side near the top to attached to

the scale.

3. To determine the Normal force add the weight of the cup to the weight of

the water; 1 ml of water weighs 1 g.

Data:

Cup	Weight (g)
Plastic
Styrofoam
Paper

Frictional Forces

• • Use the following volumes of water for the three cup types.

Cup type	Volume 1 (ml)	Volume 2 (ml)
Plastic	300	150
Styrofoam	200	100
Paper	100	50

Kinetic friction.

In this experiment you will measure the kinetic coefficient of friction for the three cups. This will be done for 2 values of normal force for each cup and each experiment will have five trials.

Tie a string around the cup and place near the bottom. You will gently pull with a spring scale attached to the string and measure force required to move the cup at a slow but steady (constant velocity) rate. This force is called the applied force. It will equal the force of friction, Fr, if there is non-accelerated motion. When a object is not accelerated it is either not moving at all or moving with a constant velocity.

Make a note on any changes in the applied force after the cup begins to move compared to the value just before the cup moved.

Results

Data tables for the friction experiment:

Plastic cup

Trial	Applied force with 200 ml of water	Applied force with 100 ml of water	Applied force/Normal force (200ml)	Applied force/Normal force (100ml)
1
2
3
4
5
Average

Styrofoam cup

Trial	Applied force with 200 ml of water	Applied force with 100 ml of water	Applied force/Normal force (200ml)	Applied force/Normal force (100ml)
1
2
3
4
5
Average

Paper cup

Trial	Applied force with 200 ml of water	Applied force with 100 ml of water	Applied force/Normal force (200ml)	Applied force/Normal force (100ml)
1
2
3
4
5
Average

Experiment 2 – Air Friction.

Air Resistance Procedure – Follow this procedure, not the one outlined in the eScience manual

1. 1. Take a single coffee filter and flatten it out.
2. 2. Hold the filter with both hands away from your body at roughly the height of your head. Measure the drop height.
3. 3. Practice dropping the filter so that it descends in a reasonably smooth fashion.
4. 4. Time five (5) drops. If possible, have a partner help you with the timings.
5. 5. Enter the drop times in the table provided in this document and calculate the average.
6. 6. From the average drop time, calculate the average speed of descent. Show your calculation in the Analysis section of this document.
7. 7. Use small pieces of tape to stick all of the filters together. My kit came with three filters.
8. 8. Repeat steps 1-6 with the “super filter.”

Data tables for the air resistance experiment:

Single filter

Trial	Drop time (sec)
1
2
3
4
5
Average

Analysis

Starting with the standard drop equation: y = ½ g we replace g with the more general acceleration value, a.

y = ½ a solving for a gives a =

Showing your work calculate a for the single filter and multi-filter.

Analysis and Discussion

Friction Experiment

Using the average values for the 5 trials in each experiment calculate the coefficient of friction for the 3 cups with both 200 ml and 100 ml of water.

Based on your experimental results, please answer the following questions:

What happened to your applied force F_app as you decreased the amount of water in the cup? Explain your answer.

How do the experimentally determined ratios of the applied and normal forces compare between cup types. Did additional weight significantly change the ratios?

How would you determine the static coefficient of friction?

Air Resistance Experiment

Draw a free body diagram for the falling coffee filter. Using the vectors from the diagram write an equation for the net force, Fnet.

Calculate the fall time of the filters assuming no air resistance. How does this fall time compare with the average fall times of the single and multi-filters?

We have assumed an accelerated motion. Without using video data how could you determine that the motion is accelerated and not one with a constant velocity?

Why does the combination reach a higher velocity? To answer this question, use your free body diagram of the falling filter and Newton’s second law to write an equation for the net force on the falling filter. Solve this equation for the acceleration and note how it depends on the mass of the falling object.

Instructors comment:

When air friction is a significant factor the equations of motion are much more complex and sometimes require methods on numerical analysis, that is, simple algebra won’t solve the equations. For many objects, especially noted are round objects such as baseballs, the force of friction depends on the square of the velocity. In many cases a falling object will reach a steady velocity, called the terminal velocity. In the case of a sky diver in a spread-eagle form that will be about 120 mph and in a tuck position it will increase to about 200 mph. With a cute deployed it can be just a few miles per hour. A bullet fired straight up (never do that) will return with a velocity of about 110 mph.

Conclusions

References