221_Friction_Proc_Fall_2010.pdf
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This experiment measures the coefficients of static and kinetic friction between a wooden block and an inclined plane. The static coefficient of friction (μs) is determined using the angle of repose method and by measuring the maximum static frictional force. The kinetic coefficient of friction (μk) is determined by measuring the frictional force needed to pull the block at constant velocity and finding the slope of a graph of frictional force versus normal force. It is also determined using the constant velocity method, where μk is equal to the tangent of the angle at which the block slides down the plane at a constant speed.
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Physics 161Static Equilibrium and Rotational Balance Intro.docx
Physics 161
Static Equilibrium and Rotational Balance
Introduction
In Part I of this lab, you will observe static equilibrium for a meter stick suspended horizontally. In Part II, you will observe the rotational balance of a cylinder on an incline. You will vary the mass hanging from the side of the cylinder for different angles.
Reference
Young and Freedman, University Physics, 12th Edition: Chapter 11, section 3
Theory
Part I: When forces act on an extended body, rotations about axes on the body can result as well as translational motion from unbalanced forces. Static equilibrium occurs when the net force and the net torque are both equal to zero. We will examine a special case where forces are only acting in the vertical direction and can therefore be summed simply without breaking them into components:
(1)
Torques may be calculated about the axis of your choosing:
(2)
where torque is specified by the equation:
(3)
where d is the lever arm (or moment arm) for the force. The lever arm is the perpendicular distance from the line of force to the axis about which you are calculating the torque.
Normally, up is "+" and down is "-" for forces. For torques, it is convenient to define clockwise as "-" and counterclockwise as "+". Whatever you decide to do, be consistent with your signs and make sure you understand what a "+" or "-" value for your force or torque means directionally.
Part II: Any round object when placed on an incline has tendency of rotating towards the bottom of an incline. If the downward force that causes the object to accelerate down the slope is canceled by another force, the object will remain stationary on the incline. Figure 1 shows the configuration of the setup. In order to have the rubber cylinder in static equilibrium we should satisfy the following conditions:
(4)
Figure 1: Experimental setup for Part II
The condition that the net force along the x-axis (which is conveniently taken along the incline) must be zero yields the relationship. (Prove this!)
Without static friction the cylinder would slide down the incline; the presence of friction causes a torque in clockwise (negative) direction. In order to have static equilibrium we need to balance that torque with a torque in counterclockwise direction. This is achieved by hanging the appropriate mass m.
Applying the last condition to the center of the cylinder will result in:
where r, the radius of the small cylinder (PVC fitting), is the moment arm for the mass m and R, the radius of the rubber cylinder, is the moment arm for the frictional force which accounts for M and m. Combining this equation with the equation for Ffr from above will result in:
(5)
(6)
By adjusting the mass m, we can observe how the equilibrium can be achieved.
Procedure
Part I: Static Equilibrium
Figure 2: Diagram of Torque Experiment Setup
1. Weigh the meter stick you use, including the metal hangers.
2. Attach .
Ah 05 b coefficient of friction(wood and felt on plastic track)
This document describes an experiment to calculate coefficients of static and kinetic friction between different surfaces using a plastic track. The experiment involves measuring frictional forces for varying normal forces using the track horizontally and as an inclined plane. Forces are measured for wood and felt surfaces of different sizes on the track. Coefficients are calculated from the slope of a graph of frictional force vs. normal force for kinetic friction and using static friction equations for static friction. Results are presented in a table comparing experimental and literature values.
Abstract Today’s experiment objectives are to determine the st.docx
Abstract
Today’s experiment objectives are to determine the stress, deflection, and the strain of a simply supported beam under load. Moreover, experimentally verify the beam stress and flexure formulas. In this week’s experiment we had to use the MTS machine in order to apply a load to a simply supported beam and measure the deflection and strain that comes out from it. As a result from the graphs we plotted, we saw that whenever the load increases, the deflection and strain also increases. We used the strain to find the theoretical stress in our calculations, and we also used the moment, moment of inertia, and the neutral axis to find the experimental stress. We calculated the moment of inertia, which came out to be 0.05122 . Also, we found the neutral axis to be 0515 in , and the maximum deflection also came out to be 0.000013 in. The maximum load applied on the beam came out to be 40049.5 psi, which we calculated from the maximum stress.
Table of Contents
Abstract……………………………………………………………..………..2
Table of Contents……………………………………….……………………3
Introduction and Theory…………………………………………………….4-6
Procedure………………………………………………….……………….7-9
Summary of Important Results…………………...………………………..10-12
Sample Calculations and Error Analysis……………….………………….13
Discussion and Conclusion………………………………………………..14-15
References……………………………………..…………………………….16
Appendix……………………………………………………….……………17
Introduction and Theory
Engineers use beams to support loads over a span length. These beams are structural
members that are only loaded non-axially causing them to be subjected to bending. “A piece is said to be in bending if the forces act on a piece of material in such a way that they tend to induce compressive stresses over one part of a cross section of the piece and tensile stresses over
the remaining part” (Ref. 1). This definition of bending is illustrated below in Figure 1.
It can be seen from Figure 1 that the compressive force, C, and the tensile force, T, acting on the member are equal in magnitude because of equilibrium. Therefore, the compressive force and the tensile force form a force couple whose moment is equal to either the tensile force multiplied by the moment arm or the compressive force multiplied by the moment arm. The moment arm is denoted, e, in Figure 1.
This is why structural members usually carry the center of the load into the tensile, compressive, or transverse loads. A beam usually carries the load transversely. During today’s experiment the load will be forced onto the beam in a symmetric order. We also must know that any cross section of the beam there will be a shear force V and a moment M. When we see in the middle of the beam we realize that the shear force diagram is zero and the moment reaches its maximum constant value.
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1 Lab 3 Newton’s Second Law of Motion Introducti.docx
1
Lab 3: Newton’s Second Law of Motion
Introduction
Newton’s Second law of motion can be summarized by the following equation:
Σ F = m a (1)
where Σ F represents a net force acting on an object, m is the mass of the object moving
under the influence of Σ F, and a is the acceleration of that object. The bold letters in
the equation represent vector quantities.
In this lab you will try to validate this law by applying Eq. 1 to the almost frictionless
motion of a car moving along a horizontal aluminum track when a constant force T
(tension in the string) acts upon it. This motion (to be exact the velocity of the moving
object) will be recorded automatically by a motion sensor. The experimental set up
for a car moving away from the motion sensor is depicted below.
If we consider the frictionless motion of the cart in the positive x-direction chosen in
the diagram, then Newton’s Second Law can be written for each of the objects as
follows:
T Ma (2)
and
– gT F ma (3)
From this system of equations we can get the acceleration of the system:
2
gF
a
m M
(4)
Because the motion of the car is not frictionless, to get better results it is necessary to
include the force of kinetic friction fk experienced by the moving car in the analysis.
When the cart is moving away from the motion detector (positive x-direction in the
diagram) Newton’s Second Law is written as follows for each of the moving objects
m and M:
1 1– kT f Ma (5)
and
1 1– gT F ma (6)
Since it is quite difficult to assess quantitatively the magnitude of kinetic friction
involved in our experiment we will solve the problem by putting the object in two
different situations in which the friction acts in opposite directions respectively while
the tension in the string remains the same.
When the cart M is forced to move towards the motion detector (negative x-direction
in the diagram), the corresponding Newton’s Second Law equations will change as
follows:
2 2kT f Ma (7)
and
2 2gT F ma (8)
Note that in equations 5, 6, 7, and 8 the direction of acceleration represented by vector
a has been chosen in the same direction as the direction of motion.
We are able to eliminate the force of kinetic friction on the final result, by calculating
the mean acceleration from these two runs:
1 2
2
ave
slope slope
a
(9)
Combing the equations (5) – (8) we derive the equation to calculate the value of
gravitational acceleration:
avea M mg
m
(10)
3
Equipment
Horizontal dynamics track with smart pulley and safety stopper on one end; collision
cart with reflector connected to a variable mass hanging over the pulley; motion
detector connected to the Science Workshop interface recording the velocity of the
moving cart.
Procedure:
a) Weigh the cart (M) and the small mass (m) hanger.
b) Open the experiment file “New ...
Simple Harmonic Oscillator Equipment No special safet.docx
Simple Harmonic Oscillator
Equipment:
No special safety equipment is required for this lab.
Computer with PASCO 850 Universal Interface and PASCO Capstone
PASCO Motion Sensor
Vertical Stand with horizontal cross bar.
Spring kit.
Mass hanger.
Set of masses.
Introduction
Imagine a spring that is suspended from a support. When no mass is attached at the end of the
spring, it has a length L (called its rest length). If a mass is added to the spring, its length increases by
∆L. The equilibrium position of the mass is now a distance L + ∆L from the spring’s support
What happens if the mass is pulled down a small distance A from the equilibrium position? The
spring exerts a restoring force, F = -kx, where x is the distance the spring is pulled down and k is the
force constant of the spring. The negative sign indicates that the force points opposite of the
direction of the displacement of the mass. The restoring force causes the mass to oscillate or move
up and down within a range of A from the equilibrium. The distance A or maximum displacement
from the equilibrium is called an amplitude of oscillation. The period of oscillation for simple
harmonic motion depends on the mass and the force constant of the spring.
We expect that the frequency of the oscillations will be found from:
𝑓 =
1
2𝜋
√
𝑘
𝑚
Here, 𝑓 is the frequency in hertz (Hz), 𝑘 is the spring constant in N/m, and 𝑚 is the mass attached to
the spring, in kg.
Another measure of the oscillations is the period. This is the time for one oscillation. It is:
𝑇 =
1
𝑓
= 2𝜋√
𝑚
𝑘
Note that the amplitude of oscillation is not present in the formulas above and, therefore, it has no
effect on the period and frequency of oscillation.
Objective
To verify the dependence of a period of a spring-mass system acting as a simple harmonic
oscillator on mass, spring constant, and amplitude.
Part #1. Measuring the Spring-Mass System
1. Suspend a green spring from a horizontal support rod and add enough mass to the other end
to stretch the spring so the coils do not touch.
2. Open “Motion Sensor Set Up” file located online next to the lab instructions.
3. Place the Motion Sensor directly under the spring and orient it at 90°.
4. Lightly tap the mass. Let it oscillate a few times so the mass hanger will move up-and-down
without much side-to-side motion. Make sure the coils don’t touch when the mass is at its
highest point. If they do, try to create a more gentle oscillation.
5. While the mass is oscillating, press Record to monitor the position of the mass relative to the
sensor over a period of several oscillations.
6. Rescale the data to fit the Graph window if necessary.
7. Using the Coordinate Tool, measure the time of five consecutive peaks.
8. Use the measured time to calculate the experimental value of the period of oscillations by
calculating the difference between two sequ
5. friction
Friction is a force that opposes motion between two surfaces in contact. There are two types of friction: static friction and kinetic friction. Static friction has a greater maximum force than kinetic friction. The laws of friction state that frictional force is proportional to the normal force and depends on the coefficient of friction, which varies based on the materials in contact. Problems involving blocks on inclined planes can be solved using the static friction force and applying equations of equilibrium. Wedges can be used to move heavy objects by applying a smaller input force, with the mechanical advantage determined by the wedge angle.
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Physics 161Static Equilibrium and Rotational Balance Intro.docx
Physics 161
Static Equilibrium and Rotational Balance
Introduction
In Part I of this lab, you will observe static equilibrium for a meter stick suspended horizontally. In Part II, you will observe the rotational balance of a cylinder on an incline. You will vary the mass hanging from the side of the cylinder for different angles.
Reference
Young and Freedman, University Physics, 12th Edition: Chapter 11, section 3
Theory
Part I: When forces act on an extended body, rotations about axes on the body can result as well as translational motion from unbalanced forces. Static equilibrium occurs when the net force and the net torque are both equal to zero. We will examine a special case where forces are only acting in the vertical direction and can therefore be summed simply without breaking them into components:
(1)
Torques may be calculated about the axis of your choosing:
(2)
where torque is specified by the equation:
(3)
where d is the lever arm (or moment arm) for the force. The lever arm is the perpendicular distance from the line of force to the axis about which you are calculating the torque.
Normally, up is "+" and down is "-" for forces. For torques, it is convenient to define clockwise as "-" and counterclockwise as "+". Whatever you decide to do, be consistent with your signs and make sure you understand what a "+" or "-" value for your force or torque means directionally.
Part II: Any round object when placed on an incline has tendency of rotating towards the bottom of an incline. If the downward force that causes the object to accelerate down the slope is canceled by another force, the object will remain stationary on the incline. Figure 1 shows the configuration of the setup. In order to have the rubber cylinder in static equilibrium we should satisfy the following conditions:
(4)
Figure 1: Experimental setup for Part II
The condition that the net force along the x-axis (which is conveniently taken along the incline) must be zero yields the relationship. (Prove this!)
Without static friction the cylinder would slide down the incline; the presence of friction causes a torque in clockwise (negative) direction. In order to have static equilibrium we need to balance that torque with a torque in counterclockwise direction. This is achieved by hanging the appropriate mass m.
Applying the last condition to the center of the cylinder will result in:
where r, the radius of the small cylinder (PVC fitting), is the moment arm for the mass m and R, the radius of the rubber cylinder, is the moment arm for the frictional force which accounts for M and m. Combining this equation with the equation for Ffr from above will result in:
(5)
(6)
By adjusting the mass m, we can observe how the equilibrium can be achieved.
Procedure
Part I: Static Equilibrium
Figure 2: Diagram of Torque Experiment Setup
1. Weigh the meter stick you use, including the metal hangers.
2. Attach .
Ah 05 b coefficient of friction(wood and felt on plastic track)
This document describes an experiment to calculate coefficients of static and kinetic friction between different surfaces using a plastic track. The experiment involves measuring frictional forces for varying normal forces using the track horizontally and as an inclined plane. Forces are measured for wood and felt surfaces of different sizes on the track. Coefficients are calculated from the slope of a graph of frictional force vs. normal force for kinetic friction and using static friction equations for static friction. Results are presented in a table comparing experimental and literature values.
Abstract Today’s experiment objectives are to determine the st.docx
Abstract
Today’s experiment objectives are to determine the stress, deflection, and the strain of a simply supported beam under load. Moreover, experimentally verify the beam stress and flexure formulas. In this week’s experiment we had to use the MTS machine in order to apply a load to a simply supported beam and measure the deflection and strain that comes out from it. As a result from the graphs we plotted, we saw that whenever the load increases, the deflection and strain also increases. We used the strain to find the theoretical stress in our calculations, and we also used the moment, moment of inertia, and the neutral axis to find the experimental stress. We calculated the moment of inertia, which came out to be 0.05122 . Also, we found the neutral axis to be 0515 in , and the maximum deflection also came out to be 0.000013 in. The maximum load applied on the beam came out to be 40049.5 psi, which we calculated from the maximum stress.
Table of Contents
Abstract……………………………………………………………..………..2
Table of Contents……………………………………….……………………3
Introduction and Theory…………………………………………………….4-6
Procedure………………………………………………….……………….7-9
Summary of Important Results…………………...………………………..10-12
Sample Calculations and Error Analysis……………….………………….13
Discussion and Conclusion………………………………………………..14-15
References……………………………………..…………………………….16
Appendix……………………………………………………….……………17
Introduction and Theory
Engineers use beams to support loads over a span length. These beams are structural
members that are only loaded non-axially causing them to be subjected to bending. “A piece is said to be in bending if the forces act on a piece of material in such a way that they tend to induce compressive stresses over one part of a cross section of the piece and tensile stresses over
the remaining part” (Ref. 1). This definition of bending is illustrated below in Figure 1.
It can be seen from Figure 1 that the compressive force, C, and the tensile force, T, acting on the member are equal in magnitude because of equilibrium. Therefore, the compressive force and the tensile force form a force couple whose moment is equal to either the tensile force multiplied by the moment arm or the compressive force multiplied by the moment arm. The moment arm is denoted, e, in Figure 1.
This is why structural members usually carry the center of the load into the tensile, compressive, or transverse loads. A beam usually carries the load transversely. During today’s experiment the load will be forced onto the beam in a symmetric order. We also must know that any cross section of the beam there will be a shear force V and a moment M. When we see in the middle of the beam we realize that the shear force diagram is zero and the moment reaches its maximum constant value.
When a beam is cur in to slices we see that if we want the moment the internal forces must be equal to the moment on the outside. So, M must be equal to the internal forces applied.
1 Lab 3 Newton’s Second Law of Motion Introducti.docx
1
Lab 3: Newton’s Second Law of Motion
Introduction
Newton’s Second law of motion can be summarized by the following equation:
Σ F = m a (1)
where Σ F represents a net force acting on an object, m is the mass of the object moving
under the influence of Σ F, and a is the acceleration of that object. The bold letters in
the equation represent vector quantities.
In this lab you will try to validate this law by applying Eq. 1 to the almost frictionless
motion of a car moving along a horizontal aluminum track when a constant force T
(tension in the string) acts upon it. This motion (to be exact the velocity of the moving
object) will be recorded automatically by a motion sensor. The experimental set up
for a car moving away from the motion sensor is depicted below.
If we consider the frictionless motion of the cart in the positive x-direction chosen in
the diagram, then Newton’s Second Law can be written for each of the objects as
follows:
T Ma (2)
and
– gT F ma (3)
From this system of equations we can get the acceleration of the system:
2
gF
a
m M
(4)
Because the motion of the car is not frictionless, to get better results it is necessary to
include the force of kinetic friction fk experienced by the moving car in the analysis.
When the cart is moving away from the motion detector (positive x-direction in the
diagram) Newton’s Second Law is written as follows for each of the moving objects
m and M:
1 1– kT f Ma (5)
and
1 1– gT F ma (6)
Since it is quite difficult to assess quantitatively the magnitude of kinetic friction
involved in our experiment we will solve the problem by putting the object in two
different situations in which the friction acts in opposite directions respectively while
the tension in the string remains the same.
When the cart M is forced to move towards the motion detector (negative x-direction
in the diagram), the corresponding Newton’s Second Law equations will change as
follows:
2 2kT f Ma (7)
and
2 2gT F ma (8)
Note that in equations 5, 6, 7, and 8 the direction of acceleration represented by vector
a has been chosen in the same direction as the direction of motion.
We are able to eliminate the force of kinetic friction on the final result, by calculating
the mean acceleration from these two runs:
1 2
2
ave
slope slope
a
(9)
Combing the equations (5) – (8) we derive the equation to calculate the value of
gravitational acceleration:
avea M mg
m
(10)
3
Equipment
Horizontal dynamics track with smart pulley and safety stopper on one end; collision
cart with reflector connected to a variable mass hanging over the pulley; motion
detector connected to the Science Workshop interface recording the velocity of the
moving cart.
Procedure:
a) Weigh the cart (M) and the small mass (m) hanger.
b) Open the experiment file “New ...
Simple Harmonic Oscillator Equipment No special safet.docx
Simple Harmonic Oscillator
Equipment:
No special safety equipment is required for this lab.
Computer with PASCO 850 Universal Interface and PASCO Capstone
PASCO Motion Sensor
Vertical Stand with horizontal cross bar.
Spring kit.
Mass hanger.
Set of masses.
Introduction
Imagine a spring that is suspended from a support. When no mass is attached at the end of the
spring, it has a length L (called its rest length). If a mass is added to the spring, its length increases by
∆L. The equilibrium position of the mass is now a distance L + ∆L from the spring’s support
What happens if the mass is pulled down a small distance A from the equilibrium position? The
spring exerts a restoring force, F = -kx, where x is the distance the spring is pulled down and k is the
force constant of the spring. The negative sign indicates that the force points opposite of the
direction of the displacement of the mass. The restoring force causes the mass to oscillate or move
up and down within a range of A from the equilibrium. The distance A or maximum displacement
from the equilibrium is called an amplitude of oscillation. The period of oscillation for simple
harmonic motion depends on the mass and the force constant of the spring.
We expect that the frequency of the oscillations will be found from:
𝑓 =
1
2𝜋
√
𝑘
𝑚
Here, 𝑓 is the frequency in hertz (Hz), 𝑘 is the spring constant in N/m, and 𝑚 is the mass attached to
the spring, in kg.
Another measure of the oscillations is the period. This is the time for one oscillation. It is:
𝑇 =
1
𝑓
= 2𝜋√
𝑚
𝑘
Note that the amplitude of oscillation is not present in the formulas above and, therefore, it has no
effect on the period and frequency of oscillation.
Objective
To verify the dependence of a period of a spring-mass system acting as a simple harmonic
oscillator on mass, spring constant, and amplitude.
Part #1. Measuring the Spring-Mass System
1. Suspend a green spring from a horizontal support rod and add enough mass to the other end
to stretch the spring so the coils do not touch.
2. Open “Motion Sensor Set Up” file located online next to the lab instructions.
3. Place the Motion Sensor directly under the spring and orient it at 90°.
4. Lightly tap the mass. Let it oscillate a few times so the mass hanger will move up-and-down
without much side-to-side motion. Make sure the coils don’t touch when the mass is at its
highest point. If they do, try to create a more gentle oscillation.
5. While the mass is oscillating, press Record to monitor the position of the mass relative to the
sensor over a period of several oscillations.
6. Rescale the data to fit the Graph window if necessary.
7. Using the Coordinate Tool, measure the time of five consecutive peaks.
8. Use the measured time to calculate the experimental value of the period of oscillations by
calculating the difference between two sequ
5. friction
Friction is a force that opposes motion between two surfaces in contact. There are two types of friction: static friction and kinetic friction. Static friction has a greater maximum force than kinetic friction. The laws of friction state that frictional force is proportional to the normal force and depends on the coefficient of friction, which varies based on the materials in contact. Problems involving blocks on inclined planes can be solved using the static friction force and applying equations of equilibrium. Wedges can be used to move heavy objects by applying a smaller input force, with the mechanical advantage determined by the wedge angle.
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Force Table Lab Partners Person 1, Person 2, Person 3, et.docx
Force Table
Lab Partners: Person 1, Person 2, Person 3, etc.
Instructor, T.A.: Your Instructor, Your TA
MM/DD/YY
ABSTRACT
This experiment was conducted to show how vectors affect one another- in particular,
how opposing vectors can be added up to cancel each other out to create a system in equilibrium,
which was done by hanging different masses over various angles on a force table. As a result,
each case showed that when summed all forces added to 0.
INTRODUCTION
Vectors are extremely important in physics, as they provide a way to show quantity that
has not only a magnitude, but a direction as well, which is extremely important when explaining
things like motion. Although these vectors are more complex than just a single number, they can
be manipulated by other vectors fairly easily. This makes combining certain measurements that
could involve a multitude of vectors, as well as manipulating a single vector as it can be added or
subtracted from itself, fairly simple.
This experiment showed the use of a force table to prove this manipulability with vectors
by setting mass as forces on certain angles in order to cancel each other out. This works as an
example because all three of the masses had some sort of force, in this case being caused by
acceleration due to gravity, being applied to them in the direction they were angled. It also
helped to demonstrate graphical methods for manipulating vectors by means of “tip-to-tail”
measurement. This type of measurement aids in the visual representation of vectors and gives
understanding to how a system of vectors looks when in equilibrium, in this case a quadrilateral
formed by four vectors of different magnitude and direction. A number of equations were used in
this experiment, and are as follows:
Instructor name.
Fx = 0Σ (1)
Fy = 0Σ (2)
Fx = Fcos( )θ (3)
Fy = Fsin( )θ (4)
g = 9.8 m/s2 (5)
F = mg (6)
Equations (1) and (2) show how F x and F y , the horizontal and vertical components of
force F (Newtons ), when in an equilibrium-system should sum to 0. Equations (3) and (4) show
how the force F is geometrically related to the horizontal and vertical components, respectively,
by means of angle (degrees ). Equation (5) is a constant that states how the acceleration due toθ
gravity, g (meters/second 2 ), is equal to 9.81. Equation (6) is a variation of Newton’s Second Law
that shows that the force due to gravity on an object is equivalent to g multiplied by mass m
(kilograms ).
PROCEDURE
The force table, which allows a central equilibrium to be reached by hanging multiple
masses at different angles, was set up with 3 points to be determined. The force table with a
3-pulley setup is seen in Figure 1. The pulleys were attached around the circumference with a
ring and three strings that could spin freely placed in the center of the table. The first trial
includ ...
To show how to measure strain and compares the result with theory of bending.
This experiment measures strain on a cantilever beam under bending loads using strain gauges. Strain gauges are electrical sensors that change resistance when experiencing strain from an applied load. The experiment applies known loads at increasing distances along the beam and measures the resulting strains. The measured strains are then compared to theoretical strain values calculated using bending formulas to relate stress, strain, moment of inertia and other mechanical properties. The results show good agreement between the measured and calculated strain values, validating the use of strain gauges and bending formulas.
Lecture Ch 04
1) Newton's laws of motion describe the relationship between forces and motion. Newton's second law states that force is equal to mass times acceleration (F=ma).
2) Newton's third law states that for every action force there is an equal and opposite reaction force.
3) Friction is a force that opposes motion between two surfaces in contact. The coefficient of friction determines the maximum static and kinetic friction forces.
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- http://www.ninetyeast.net/physics/university/mechanics-of-materials/what-is-stress/what-is-normal-stress
- http://www.ninetyeast.net/physics/university/mechanics-of-materials/what-is-stress/what-is-normal-stress/normal-stress-examples
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Lab Partners: Person 1, Person 2, Person 3, etc.
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MM/DD/YY
ABSTRACT
This experiment was conducted to show how vectors affect one another- in particular,
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which was done by hanging different masses over various angles on a force table. As a result,
each case showed that when summed all forces added to 0.
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by setting mass as forces on certain angles in order to cancel each other out. This works as an
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helped to demonstrate graphical methods for manipulating vectors by means of “tip-to-tail”
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Instructor name.
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includ ...
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- 1. Experiment 6 The Coefficient of Friction Equipment: 1 ULI with force probe 1 Inclined plane (see Fig. 6-1) 1 Wooden block 1 Triple beam balance Masses Pulley Objectives: To measure the coefficients of static and kinetic friction between a wooden block and a wooden plane. Theory Friction is the force that resists the relative motion of one surface in contact with another. There are two types of friction: static and kinetic. Usually, the kinetic frictional force is less than the maximum value of the static frictional force. The maximum value of static frictional force is given by fs,max = µs N and the kinetic frictional force is given by fk = µk N , where µs is the coefficient of static friction, µk is the coefficient of kinetic friction and N is the normal force. If f k versus N is graphed, the slope of the line is µk for the system. Similarly, if fs,max versus N is graphed, the slope of the line is µs . The angle of repose is defined as the angle at which an object just starts to slide down an inclined plane. If ! is the angle of repose, it can be shown that µs = tan! . We will call this method to determine the static coefficient of friction the angle of repose method. It can also be shown that when an object slides down an incline at constant velocity, µk = tan! . In this experiment, the frictional force between a wooden block and the wooden surface of a horizontal and inclined plane will be measured, and from these plotted data, the coefficients of static and kinetic friction will be obtained. The angle of repose method will also be used to determine the coefficient of static friction. Lastly, the coefficient of kinetic friction will be determined by a second method (called constant velocity method) by noting the angle ! that the block slides down an incline without accelerating and then using µk = tan! . Procedure: 1. Turn on the ULI and the computer. Open the Logger Pro application. Go to the Experiment/Setup sensors/LabPro1 menu and choose the port which force probe sensor is plugged in. Go through list of probes and highlight Dual Range 50N Force Probe. Figure 1- Block on incline plane
- 2. 2. Calibrate the force probe by using the path Experiment/Calibrate/LabPro1: Dual Range Force. Click on calibrate now and follow the directions given to you on the screen. Use 1/2 kilogram on the weight hanger for the calibration. Be sure to use units of force (not mass) when calibrating the force probe. 3. Measure the mass of the wooden block with the Triple-Beam balance and calculate its weight in newtons. 4. With plane in the horizontal position, place 500 grams on the block and pull the block across the plane at a constant speed with the force probe. Be sure to pull horizontally. Note the "bump" at the start of the graph. This peak represents a maximum force which can be used to calculate µs . See fig 6-2 below and theory section. 5. Highlight the constant force portion of your run. Determine the mean force. The force needed to pull the block is your frictional force and the combined weight of the block and mass is your normal force. Note that normal force here is also used in step 4 to determine µs . 6. Repeat steps 4 & 5, adding 500 grams each time until a total of 3000 grams has been added to the block. Record the frictional and normal forces needed for each trial. 7. Plot a graph of the frictional force vs. the normal force using Graphical Analysis, with the frictional force on the Y axis and the normal force on the X axis. Plot a "best fit line" between the points by pulling down the Graph menu to Regression line. To obtain the slope of this line, pull down the Graph menu to Statistics. This will print the value of the slope at the bottom of the graph. If Ffr, the frictional force is proportional to FN, the normal force (Ffr=µkFN), then the slope of this line should be the coefficient of kinetic friction between the two surfaces. Determine this value from the graph. Block on an inclined plane 8. Calculate the force needed to pull the block up a plane inclined to 300 at a constant speed when loaded with 500 grams. Draw a force diagram labeling all the forces acting on the block as it moves up the inclined plane. Use the coefficient obtained from your graph. 9. Measure the force needed to pull the block up the plane (same angle as part 8) at a constant speed. If there is a large difference between the calculated and the experimental values, check the calculations carefully. (Common mistakes: Neglecting the mass of the block and improper force diagrams) Calculate the percentage difference between this value and the calculated value. Angle of repose method 10. Add 500 g to block. Find the coefficient of static friction by slowly raising the incline plane until the block just starts to slide. Note the angle and use µs = tan! . Repeat with 1000g total added to block. Remove mass(es). Constant Velocity Method 11. Add 500g to block. Find kinetic coefficient of friction by tilting the inclined plane and noting the angle at which the block slides at a constant
- 3. Experiment 6 The Coefficient of Friction speed. You should have to tap the block in order to get it started. Use µk = tan!. Add a total of 1000g to block and repeat this step. Questions: 1. Show that µk=tanθ for the constant velocity method. Include a diagram of all the forces on the block as it slides down the inclined plane. 2. When the mass on the block is was doubled, what happens to the angle of repose? Were your results as expected. Explain. 3. Why was it necessary to tap the block to get it started in section 11 of the lab? 4. Why can anti-lock brakes stop a car in a shorter distance than regular brakes? 5. Which method do you think would yield the more accurate value for the coefficient of kinetic friction and why? Force (Newtons) Time (sec) figure 6-2