PHYS 1100 LESSON 8 FOR
TUESDAY, AUGUST 17, 2010
I Introduction
II Logistics – Running Grades
III Turn in Assignments Due and Return of Papers
IV Review of Lesson 7: Energy, Momentum, Torque, et al
Energy: interchangeable with mass, per
Einstein’s E = mc2.
41H1 = 2He4 + mc2 + 2b+.
F d = using energy = Joules. Work is useful energy. Efficiency, e = W/E, e<1
Natural gas: CH4 + 2O2 = CO2 + 2H2O + Energy
Gasoline: 2C8H18 + 25O2 =
16CO2 + 18H2O + Energy
Momentum, p = m v goes in a straight line
Angular momentum, l = m v r
V Lesson 8: Inertia, Torque, Gravity
A. Inertia is kg m2.
B. Torque is N-m
C. Gravity:
1. Kepler – P2 (m + M) = [(4 p2)/G] r3.
This is Kepler’s 3rd law dealing with the period of a planet, P, with a mass, m, traveling around the Sun, with a mass, M, at a distance between the Sun and the planet equaling “r”. However, it applies to moons, asteroids, stars, satellites, blah blah.
Period is in seconds, mass in kilograms, distance in meters (mks). The Universal Gravitational Constant is G = 6.67 x 10-11 N m2 / kg2.
2. Newton – F = GmM/r2.
This part of Newton’s 2nd Law, which deals with the force, F, of gravity.
Little ‘m’ is the mass of a smaller object, such as human; big “M” is the mass of the larger object, such as planet Earth; r is the distance between the center of the first object (like a human’s navel) and the center of the second object (like the distance from the human to Earth’s core, i.e., the radius of Earth.
As a force, instead of a period, this law applies both to moving objects, like planets, moons, stars; and to object that are not moving, like people standing on Earth, or between two bowling balls in a bowling alley.
The Universal Gravitational Constant is G = 6.67 x 10-11 N m2 / kg2.
VI Laboratory Exercise 8: Simple Harmonic Motion
VII HWK Assignment 3: 10-14 and do Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, and 65 on pp 323-327; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, 65 and 77 on pp 366-371; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53 and 63 on pp 409-412; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, and 65 on pp 445-448; and Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, 67, 69, and 77 on pp 491-495; due 8/19
VIII Essay 3: James Prescott Joule, due 8/19
Tuesday, August 17, 2010
LAB 8
PhysicsLab8 Tuesday, August 17, 2010 Name __________________
Dr Dave Menke, Instructor
I Title: Simple Harmonic Motion
II Purpose: Study Simple Harmonic Motion using a plumb bob pendulum.
III Equipment
1. String, yarn, or cord ≥ 1.0 meter long (or as close as possible)
2. Weight - to make a plumb bob pendulum (washers?)
3. Stop Watch, face watch, digital watch, clock, or other chronometer
4. Meter stick or metric ruler
5. Protractor
IV Procedure (Some of this is similar to the Gravity lab)
1. Obtain, or make, a length of string or cord that is very close to 1.00 meter long. Slightly longer is better than slightly shorter.
2. Attach a weight to one end of the string to create a plumb bob, that we will call Bob.
3. Attach the other end of the string to some stationary object (door hinge, ceiling, weighted ring stand, etc.). Do NOT use a primate because it is not stable or other mammal to hold Bob because it is not stable.
4. Measure the length of Bob exactly (to the closest millimeter) after you have set it up. This will be from the point of connection on top to the middle of the weight. Record this length (we will call the length “r”) as accurately as possible.
5. Put the Data in the Table below; one column is for the number of the trials; another for the time (in seconds) for each cycle. And a third column for amplitude in the x-direction.
6. Have one of the lab partners pull the pendulum back, to an angle of θ = 45° (try to be exact; use protractor) as seen in the diagram a
7. Measure the x-component of the Bob's motion. If the string pendulum is exactly 1.0 meter long, and if the angle is exactly 45°, then the x-component will be (1.0 m) Sin 45° = 0.707 m = 70.7 cm. Thus, when you measure the x-component, it will be very close to 70 cm. This will be your original (and maximum) amplitude.
8. Simultaneously, release Bob and depress the stop watch button to start the time “running.” It is best to have the same homosapien release Bob and operate the stopwatch (the same brain controls both hands).
9. Allow Bob to swing freely as long it can. Every time that it returns to its starting point, note and record the time, and the distance. For example, at t = 0.00 s, the x-component will be (about) 70 cm. The next time that it comes back, about 1.8 seconds later, the x-component will be less, maybe 65 cm; next time, maybe 60 cm; and so forth. If you find it very difficult to do both the time and the x-component distance, you may substitute that data that you gathered for Lab #2 about Gravity. Keep the pendulum swinging until it stops, or, nearly stops. If you need to create another table to extend the data, please do so.
10. When done with gathering the data, plot the data points on a graph, with time in seconds, t, along the horizontal (left-right) and amplitude (length of x) along the vertical. Connect the dots as smoothly as you can.
11. Determine the period of oscillation using the graph of data.
V Data & Calculations:
Trial Time (sec) Amplitude (cm)
VI Results:
The purpose if this laboratory (Example of Simple Harmonic Motion) was / was not achieved due to:
VII Error Analysis:
A. Quantitative Error: NA
B. Qualitative Error:
1. Personal -
2. Random -
3. Systematic –
VIII Questions:
1. What is the period of oscillation?
2. What is the maximum amplitude?
3. What is the average periodic decrease in amplitude for each cycle?
4. List 4 items in your life and your world that oscillate.
Dr Dave Menke, Instructor
I Title: Simple Harmonic Motion
II Purpose: Study Simple Harmonic Motion using a plumb bob pendulum.
III Equipment
1. String, yarn, or cord ≥ 1.0 meter long (or as close as possible)
2. Weight - to make a plumb bob pendulum (washers?)
3. Stop Watch, face watch, digital watch, clock, or other chronometer
4. Meter stick or metric ruler
5. Protractor
IV Procedure (Some of this is similar to the Gravity lab)
1. Obtain, or make, a length of string or cord that is very close to 1.00 meter long. Slightly longer is better than slightly shorter.
2. Attach a weight to one end of the string to create a plumb bob, that we will call Bob.
3. Attach the other end of the string to some stationary object (door hinge, ceiling, weighted ring stand, etc.). Do NOT use a primate because it is not stable or other mammal to hold Bob because it is not stable.
4. Measure the length of Bob exactly (to the closest millimeter) after you have set it up. This will be from the point of connection on top to the middle of the weight. Record this length (we will call the length “r”) as accurately as possible.
5. Put the Data in the Table below; one column is for the number of the trials; another for the time (in seconds) for each cycle. And a third column for amplitude in the x-direction.
6. Have one of the lab partners pull the pendulum back, to an angle of θ = 45° (try to be exact; use protractor) as seen in the diagram a
7. Measure the x-component of the Bob's motion. If the string pendulum is exactly 1.0 meter long, and if the angle is exactly 45°, then the x-component will be (1.0 m) Sin 45° = 0.707 m = 70.7 cm. Thus, when you measure the x-component, it will be very close to 70 cm. This will be your original (and maximum) amplitude.
8. Simultaneously, release Bob and depress the stop watch button to start the time “running.” It is best to have the same homosapien release Bob and operate the stopwatch (the same brain controls both hands).
9. Allow Bob to swing freely as long it can. Every time that it returns to its starting point, note and record the time, and the distance. For example, at t = 0.00 s, the x-component will be (about) 70 cm. The next time that it comes back, about 1.8 seconds later, the x-component will be less, maybe 65 cm; next time, maybe 60 cm; and so forth. If you find it very difficult to do both the time and the x-component distance, you may substitute that data that you gathered for Lab #2 about Gravity. Keep the pendulum swinging until it stops, or, nearly stops. If you need to create another table to extend the data, please do so.
10. When done with gathering the data, plot the data points on a graph, with time in seconds, t, along the horizontal (left-right) and amplitude (length of x) along the vertical. Connect the dots as smoothly as you can.
11. Determine the period of oscillation using the graph of data.
V Data & Calculations:
Trial Time (sec) Amplitude (cm)
VI Results:
The purpose if this laboratory (Example of Simple Harmonic Motion) was / was not achieved due to:
VII Error Analysis:
A. Quantitative Error: NA
B. Qualitative Error:
1. Personal -
2. Random -
3. Systematic –
VIII Questions:
1. What is the period of oscillation?
2. What is the maximum amplitude?
3. What is the average periodic decrease in amplitude for each cycle?
4. List 4 items in your life and your world that oscillate.
Monday, August 16, 2010
LESSON 7
PHYS 1100 LESSON 7 FOR
MONDAY, AUGUST 16, 2010
I Introduction
II Logistics – Running Grades
III Turn in Assignments Due and Return of Papers
IV Review of Lesson 6: Energy, Work, Momentum, Angular Momentum, Impulse
Energy: interchangeable with mass, per
Einstein’s E = mc2.
41H1 = 2He4 + mc2 + 2b+.
F d = using energy = Joules. Work is useful energy. Efficiency, e = W/E, e<1
Natural gas: CH4 + 2O2 = CO2 + 2H2O + Energy
Gasoline: 2C8H18 + 25O2 =
16CO2 + 18H2O + Energy
Momentum, p = m v goes in a straight line
Angular momentum, l = m v r
V Lesson 7: Torque, Inertia, Impulse
Impulse = I = F Dt. Baseball, golf, billiards, tennis. N-s units of Impulse
F = m a
I = (ma) Dt = m(a Dt) = m (Dv/Dt)(Dt) = m(Dv)( Dt/Dt) = mDv = p
Example: What force does a baseball hitter use when he hits a 0.15 kg ball, traveling at 160 km/hour, and the contact time, Dt = 0.12 sec?
m v = F Dt
So, WTF?
(m)(v)/(dt) = F = (0.15)(44.5)/(0.12) = 55.625 N
160 km/hr = (5/18)(160 km/h) m/s 44.5 m/s
55.625 N = 56 N ~ 5.6 E1 or x 10^1 or 101 N.
Torque has the name units as Energy; torque, t, = r F; N-m
Inertia = characteristic of matter that resists change units are kg m2.
VI Laboratory Exercise 7: PE KE
VII HWK Assignment 3: 10-14 and do Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, and 65 on pp 323-327; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, 65 and 77 on pp 366-371; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53 and 63 on pp 409-412; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, and 65 on pp 445-448; and Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, 67, 69, and 77 on pp 491-495; due 8/19
VIII Essay 3: James Prescott Joule, due 8/19
MONDAY, AUGUST 16, 2010
I Introduction
II Logistics – Running Grades
III Turn in Assignments Due and Return of Papers
IV Review of Lesson 6: Energy, Work, Momentum, Angular Momentum, Impulse
Energy: interchangeable with mass, per
Einstein’s E = mc2.
41H1 = 2He4 + mc2 + 2b+.
F d = using energy = Joules. Work is useful energy. Efficiency, e = W/E, e<1
Natural gas: CH4 + 2O2 = CO2 + 2H2O + Energy
Gasoline: 2C8H18 + 25O2 =
16CO2 + 18H2O + Energy
Momentum, p = m v goes in a straight line
Angular momentum, l = m v r
V Lesson 7: Torque, Inertia, Impulse
Impulse = I = F Dt. Baseball, golf, billiards, tennis. N-s units of Impulse
F = m a
I = (ma) Dt = m(a Dt) = m (Dv/Dt)(Dt) = m(Dv)( Dt/Dt) = mDv = p
Example: What force does a baseball hitter use when he hits a 0.15 kg ball, traveling at 160 km/hour, and the contact time, Dt = 0.12 sec?
m v = F Dt
So, WTF?
(m)(v)/(dt) = F = (0.15)(44.5)/(0.12) = 55.625 N
160 km/hr = (5/18)(160 km/h) m/s 44.5 m/s
55.625 N = 56 N ~ 5.6 E1 or x 10^1 or 101 N.
Torque has the name units as Energy; torque, t, = r F; N-m
Inertia = characteristic of matter that resists change units are kg m2.
VI Laboratory Exercise 7: PE KE
VII HWK Assignment 3: 10-14 and do Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, and 65 on pp 323-327; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, 65 and 77 on pp 366-371; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53 and 63 on pp 409-412; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, and 65 on pp 445-448; and Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, 67, 69, and 77 on pp 491-495; due 8/19
VIII Essay 3: James Prescott Joule, due 8/19
LAB 7
PhysicsLab7 Monday August 16, 2010 Name __________________
Dr Dave Menke, Instructor
I Title: Potential vs. Kinetic Energy
II Purpose: To investigate the difference between potential energy and kinetic energy by using “elastic” bouncing spheres.
III Equipment:
* One “elastic” bouncing sphere of 8.5 gram mass or 32.4 grams
* Metric ruler
* Pen, calculator, lab book, etc.
IV Procedure
1. Raise the elastic sphere to h1 = 2.0 meters above the lab floor.
2. Calculate the potential energy of the elastic sphere, PE = mgh1, by placing the first elastic sphere on the ground, and then lifting it up two meters. Record. This will be in JOULES.
3. Calculate the amount of time that it takes for the elastic sphere to fall 2.0 meters. Remember the “free fall” relationship: h1 = ½ g t2. You already know h = 2.0 meters. And g = 9.8 m/s2. Record.
4. Calculate the final velocity for the elastic sphere, vf, using the relationship that vf2 – vi2 = 2 g h1. Since vi = 0, vf = √(2 g h1) = √[(2)(9.8)(2.0)]. Record.
5. Calculate the Kinetic Energy of the elastic sphere just before impact. KE = ½ m vf2. Record.
6. Compare the KE in #5 with the PE in #2. Which is larger, or are they equal? Explain why.
7. Place the elastic sphere at h1 = 2.0 meters above the floor. Release the elastic sphere. Measure how high the elastic sphere rebounds after it hits the floor, h2. Record.
8. Repeat 4 more times, for a total of 5 times. Take the average of the rebound, h2. Record.
9. Using DPE = m g (Dh), find out how much energy was “lost” by the elastic sphere when it bounced up. Remember, Dh = h1 – h2.
10. List places that the energy “went.”
V Data & Calculations
1. Mass of elastic sphere: _________grams; convert to kg____________
2. Initial PE = mgh1 = ____________ joules
3. Time for sphere to fall 2.0 meters: _________ seconds.
4. The final velocity, vf : ____________ m/s.
5. Kinetic energy: ___________ Joules
6. The difference between PE and KE, in joules: ________J.
7. The average change in height (the average of the 5 trials): _________ meters.
8. The final PE after the rebound, m g h2 : ________
9. Subtract the final PE in #8 from the initial PE in #2. DPE = __________ joules.
VI Results
Explain if there were a difference between PE and KE, and why. Also, explain where the “lost energy” went.
VII Error Analysis
A. Quantitative Error –
The true laboratory value of final velocity, vf(true) = 6.261 m/s; the lab value for the mean velocity is vave = 3.131 m/s.
% Error = [ |v(true) – v (yours)| / v(true) ] x 100%
B. Qualitative Error: Sources of Error
Personal
Systematic
Random
VIII Questions
Spheres made of rubber cause collisions that are somewhat elastic. a. name objects where the collisions would be almost perfectly elastic; b. name objects where the collisions would be almost entirely inelastic.
In light of these concepts, why do you think that some football players are “light” and others are very heavy and muscular?
Dr Dave Menke, Instructor
I Title: Potential vs. Kinetic Energy
II Purpose: To investigate the difference between potential energy and kinetic energy by using “elastic” bouncing spheres.
III Equipment:
* One “elastic” bouncing sphere of 8.5 gram mass or 32.4 grams
* Metric ruler
* Pen, calculator, lab book, etc.
IV Procedure
1. Raise the elastic sphere to h1 = 2.0 meters above the lab floor.
2. Calculate the potential energy of the elastic sphere, PE = mgh1, by placing the first elastic sphere on the ground, and then lifting it up two meters. Record. This will be in JOULES.
3. Calculate the amount of time that it takes for the elastic sphere to fall 2.0 meters. Remember the “free fall” relationship: h1 = ½ g t2. You already know h = 2.0 meters. And g = 9.8 m/s2. Record.
4. Calculate the final velocity for the elastic sphere, vf, using the relationship that vf2 – vi2 = 2 g h1. Since vi = 0, vf = √(2 g h1) = √[(2)(9.8)(2.0)]. Record.
5. Calculate the Kinetic Energy of the elastic sphere just before impact. KE = ½ m vf2. Record.
6. Compare the KE in #5 with the PE in #2. Which is larger, or are they equal? Explain why.
7. Place the elastic sphere at h1 = 2.0 meters above the floor. Release the elastic sphere. Measure how high the elastic sphere rebounds after it hits the floor, h2. Record.
8. Repeat 4 more times, for a total of 5 times. Take the average of the rebound, h2. Record.
9. Using DPE = m g (Dh), find out how much energy was “lost” by the elastic sphere when it bounced up. Remember, Dh = h1 – h2.
10. List places that the energy “went.”
V Data & Calculations
1. Mass of elastic sphere: _________grams; convert to kg____________
2. Initial PE = mgh1 = ____________ joules
3. Time for sphere to fall 2.0 meters: _________ seconds.
4. The final velocity, vf : ____________ m/s.
5. Kinetic energy: ___________ Joules
6. The difference between PE and KE, in joules: ________J.
7. The average change in height (the average of the 5 trials): _________ meters.
8. The final PE after the rebound, m g h2 : ________
9. Subtract the final PE in #8 from the initial PE in #2. DPE = __________ joules.
VI Results
Explain if there were a difference between PE and KE, and why. Also, explain where the “lost energy” went.
VII Error Analysis
A. Quantitative Error –
The true laboratory value of final velocity, vf(true) = 6.261 m/s; the lab value for the mean velocity is vave = 3.131 m/s.
% Error = [ |v(true) – v (yours)| / v(true) ] x 100%
B. Qualitative Error: Sources of Error
Personal
Systematic
Random
VIII Questions
Spheres made of rubber cause collisions that are somewhat elastic. a. name objects where the collisions would be almost perfectly elastic; b. name objects where the collisions would be almost entirely inelastic.
In light of these concepts, why do you think that some football players are “light” and others are very heavy and muscular?
LESSON 6
PHYS 1100 LESSON 6 FOR
THURSDAY, AUGUST 12, 2010
I Introduction
II Logistics
III Turn in Assignments Due: Homework 1, 2, Essay 1, 2, etc. and Return of Papers
IV Test 2
V Mind Game 2
VI Review of Lesson 5: Hooke's Law, Energy, Work, Momentum
F = - k x
F = - k y = m g
Energy: heat, light, mechanical, acoustical, etc.
Kinetic, Potential, ….
Work / Energy < 1
F x d = energy, units 1.0 N-m == Joule
4.186 calorie = 1 joule
Momentum = energy of motion
p = m v
Dp = 0 in a closed system
E = F x d (in Joules)
PE = m g h (in Joules)
KE = ½ m v2 (in Joules)
p = m v (in kg m/s)
Ff = m m g (friction)
VII Lesson 6: Momentum, Impulse, Conservation, Angular Momentum
p = m v
S p = constant in a closed system, or,
Dp = 0 in a closed system
F Dt = Impulse, but same units as momentum
l = m v r = p r this is angular momentum
t = r x F this is torque
VIII Laboratory Exercise 6: Hooke's Law
IX Homework Assignment 3: Read Chapters 10-14 and do Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, and 65 on pp 323-327; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, 65 and 77 on pp 366-371; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53 and 63 on pp 409-412; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, and 65 on pp 445-448; and Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, 67, 69, and 77 on pp 491-495; due 8/19
X Essay 3: James Prescott Joule, due 8/19
THURSDAY, AUGUST 12, 2010
I Introduction
II Logistics
III Turn in Assignments Due: Homework 1, 2, Essay 1, 2, etc. and Return of Papers
IV Test 2
V Mind Game 2
VI Review of Lesson 5: Hooke's Law, Energy, Work, Momentum
F = - k x
F = - k y = m g
Energy: heat, light, mechanical, acoustical, etc.
Kinetic, Potential, ….
Work / Energy < 1
F x d = energy, units 1.0 N-m == Joule
4.186 calorie = 1 joule
Momentum = energy of motion
p = m v
Dp = 0 in a closed system
E = F x d (in Joules)
PE = m g h (in Joules)
KE = ½ m v2 (in Joules)
p = m v (in kg m/s)
Ff = m m g (friction)
VII Lesson 6: Momentum, Impulse, Conservation, Angular Momentum
p = m v
S p = constant in a closed system, or,
Dp = 0 in a closed system
F Dt = Impulse, but same units as momentum
l = m v r = p r this is angular momentum
t = r x F this is torque
VIII Laboratory Exercise 6: Hooke's Law
IX Homework Assignment 3: Read Chapters 10-14 and do Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, and 65 on pp 323-327; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, 65 and 77 on pp 366-371; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53 and 63 on pp 409-412; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, and 65 on pp 445-448; and Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, 67, 69, and 77 on pp 491-495; due 8/19
X Essay 3: James Prescott Joule, due 8/19
LAB 6
Physics Lab 6 Thursday, August 12, 2010 Name __________________
I Title: Acceleration of Gravity
II Purpose: To determine the acceleration of gravity using simple equipment.
III Equipment
1. String, yarn, or cord ≥ 1.0 meter long (or as close as possible)
2. Weight - to make a plumb bob pendulum (washers?)
3. Stop Watch, face watch, digital watch, clock, or other chronometer
4. Meter stick or metric ruler
5. Weighted Ring Stand Optional
IV Procedure
Obtain, or make, a length of string or cord that is very close to 1.00 meter long. Slightly longer is better than slightly shorter.
Attach a weight to one end of the string to create a plumb bob, that we will call Bob.
Have that same person, or another, attach the other end of the string to some stationary object (door hinge, ceiling, weighted ring stand, etc.). Do NOT use a primate because it is not stable or other mammal to hold Bob because it is not stable.
Measure the length of Bob exactly (to the closest millimeter) after you have set it up. This will be from the point of connection on top to the middle of the weight. Record this length (we will call the length “y”) as accurately as possible.
Use the Data Table below; one column is for the number of the trials; the other for the time (in seconds) for each cycle.
6. Have one of the lab partners pull the pendulum back, to about an angle of θ = 45° (but no further) as seen in the diagram to the right
Simultaneously, release Bob and depress the stop watch button to start the time “running.” It is best to have the same homosapien release Bob and operate the stopwatch (the same brain controls both hands).
Allow Bob to swing out and come back to where it was released. Stop the watch. That is one cycle. Record the time in the table. Reset the watch and get ready to repeat.
Have the same CroMagnon Repeat steps #6 - #8, nine more times, and place your data in the table. You should have a total of ten trials.
Find the average period of oscillation of the ten trials. This means, add up all the numbers in the second column, then divide by 10. Record.
Use the data to find the acceleration of Earth’s gravity, g, by re-writing Galileo’s Period-Length equation so that the acceleration, g, is all alone on the left side.
-MORE-
Physics Lab 6 Thursday, August 12, 2010 page 2 Name _____________
P = 2 p [(y / g)] ½
P is the period in seconds, y is the length in meters, and g is what we want to find. It will be in meters per square second. This equation reads “Period equals two times pi times the square root of (y/g).”
Let’s continue to re-write this relationship, in order for us to get, g all alone:
[P / 2 p ] = [(y / g)] ½
[P / 2 p ]2 = (y / g)
g = y [2 p / P] 2
Remember that “y” is the length of the string (about 1.0 meter, but make sure it’s exactly measured), and “P” is the average period of time that you found by combining the 10 periods above. And, of course, p = 3.14.
V Data & Calculations:
1. Exact length of string, in meters: _______________
Table of Data
Trial # Time (seconds) Trial # Time (seconds)
1 6
2 7
3 8
4 9
5 10
Average Period of Oscillation of these ten trials (seconds)
P = __________________
YOUR acceleration of gravity, in m/s2:
g = y [2 p / P] 2 = ______________________
-MORE-
Physics Lab 6 Thursday, August 12, 2010 page 3 Name _____________
The true value of acceleration is g0 = - 9.8 m/s2.
VI Results:
The purpose of determining the acceleration of gravity using the equipment and procedures above was or was not achieved due to: (explain in detail)
VII Error Analysis:
A. Qualitative Error:
Personal: (what did you or your partner do to screw up?)
Systematic: (what external factors happened that you could not control, e.g., broken equipment, doing the lab in a hurricane, etc.)
Random: There is always random error, unless one does multiple trials. Since we did 10 trials and took an average, there is NO random error in this lab.
B. Quantitative Error:
Find the quantitative error for this experiment: (% error). Find this by using the error analysis formula:
|[True Answer – Your Answer]| / [True Answer] x 100% = ________%
Remember, the true value of acceleration is g0 = - 9.8 m/s2.
VIII Questions
Information: The acceleration of gravity, g, for any planet, is equal to: g = GM / R2 where G is the universal constant of Gravity = 6.67 x 10-11 Nm2/kg2; M is the mass of any planet given, and R is the radius of any planet given. You are dividing GM by the square of R = R2.
1. The mass of Mars is M = 6.4 x 1023 kg; the radius of Mars is R = 3.4 x 106 meters. Find the acceleration of gravity of Mars, g♂.
2. The mass of Jupiter is M = 1.9 x 1027 kg ; the radius of Jupiter is R = 7.13 x 107 m . Find the acceleration of gravity of Jupiter, g♃.
END
I Title: Acceleration of Gravity
II Purpose: To determine the acceleration of gravity using simple equipment.
III Equipment
1. String, yarn, or cord ≥ 1.0 meter long (or as close as possible)
2. Weight - to make a plumb bob pendulum (washers?)
3. Stop Watch, face watch, digital watch, clock, or other chronometer
4. Meter stick or metric ruler
5. Weighted Ring Stand Optional
IV Procedure
Obtain, or make, a length of string or cord that is very close to 1.00 meter long. Slightly longer is better than slightly shorter.
Attach a weight to one end of the string to create a plumb bob, that we will call Bob.
Have that same person, or another, attach the other end of the string to some stationary object (door hinge, ceiling, weighted ring stand, etc.). Do NOT use a primate because it is not stable or other mammal to hold Bob because it is not stable.
Measure the length of Bob exactly (to the closest millimeter) after you have set it up. This will be from the point of connection on top to the middle of the weight. Record this length (we will call the length “y”) as accurately as possible.
Use the Data Table below; one column is for the number of the trials; the other for the time (in seconds) for each cycle.
6. Have one of the lab partners pull the pendulum back, to about an angle of θ = 45° (but no further) as seen in the diagram to the right
Simultaneously, release Bob and depress the stop watch button to start the time “running.” It is best to have the same homosapien release Bob and operate the stopwatch (the same brain controls both hands).
Allow Bob to swing out and come back to where it was released. Stop the watch. That is one cycle. Record the time in the table. Reset the watch and get ready to repeat.
Have the same CroMagnon Repeat steps #6 - #8, nine more times, and place your data in the table. You should have a total of ten trials.
Find the average period of oscillation of the ten trials. This means, add up all the numbers in the second column, then divide by 10. Record.
Use the data to find the acceleration of Earth’s gravity, g, by re-writing Galileo’s Period-Length equation so that the acceleration, g, is all alone on the left side.
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Physics Lab 6 Thursday, August 12, 2010 page 2 Name _____________
P = 2 p [(y / g)] ½
P is the period in seconds, y is the length in meters, and g is what we want to find. It will be in meters per square second. This equation reads “Period equals two times pi times the square root of (y/g).”
Let’s continue to re-write this relationship, in order for us to get, g all alone:
[P / 2 p ] = [(y / g)] ½
[P / 2 p ]2 = (y / g)
g = y [2 p / P] 2
Remember that “y” is the length of the string (about 1.0 meter, but make sure it’s exactly measured), and “P” is the average period of time that you found by combining the 10 periods above. And, of course, p = 3.14.
V Data & Calculations:
1. Exact length of string, in meters: _______________
Table of Data
Trial # Time (seconds) Trial # Time (seconds)
1 6
2 7
3 8
4 9
5 10
Average Period of Oscillation of these ten trials (seconds)
P = __________________
YOUR acceleration of gravity, in m/s2:
g = y [2 p / P] 2 = ______________________
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Physics Lab 6 Thursday, August 12, 2010 page 3 Name _____________
The true value of acceleration is g0 = - 9.8 m/s2.
VI Results:
The purpose of determining the acceleration of gravity using the equipment and procedures above was or was not achieved due to: (explain in detail)
VII Error Analysis:
A. Qualitative Error:
Personal: (what did you or your partner do to screw up?)
Systematic: (what external factors happened that you could not control, e.g., broken equipment, doing the lab in a hurricane, etc.)
Random: There is always random error, unless one does multiple trials. Since we did 10 trials and took an average, there is NO random error in this lab.
B. Quantitative Error:
Find the quantitative error for this experiment: (% error). Find this by using the error analysis formula:
|[True Answer – Your Answer]| / [True Answer] x 100% = ________%
Remember, the true value of acceleration is g0 = - 9.8 m/s2.
VIII Questions
Information: The acceleration of gravity, g, for any planet, is equal to: g = GM / R2 where G is the universal constant of Gravity = 6.67 x 10-11 Nm2/kg2; M is the mass of any planet given, and R is the radius of any planet given. You are dividing GM by the square of R = R2.
1. The mass of Mars is M = 6.4 x 1023 kg; the radius of Mars is R = 3.4 x 106 meters. Find the acceleration of gravity of Mars, g♂.
2. The mass of Jupiter is M = 1.9 x 1027 kg ; the radius of Jupiter is R = 7.13 x 107 m . Find the acceleration of gravity of Jupiter, g♃.
END
Tuesday, August 10, 2010
LESSON 5
PHYS 1100 LESSON 5 FOR
TUESDAY, AUGUST 10, 2010
I Introduction
II Logistics
III Return of tests, labs, papers; collection of overdue assignments
IV Running Grades
V Review of Lesson 4: Newton's Laws of Motion
A. Objects at rest, stay at rest; objects in motion stay in motion; UNLESS acted upon by an Fext.
B. F = m a à ties into the Universal Law of Gravity
C. Every force has an equal and opposite force, or, F1 = - F2.
D. Units of force are “Newtons”, kg m/s2. = N
F = ma
v = x/t
VI Lesson 5: Forces
A. The force of friction, Ff = mN = + mmg, which means the force of friction equals a number (m) that is called the “coefficient of friction” multiplied by the equal and opposite force to gravity, N, the Normal force; or N = mg, where m is the “mass” and g is the acceleration of gravity, “9.8 m/s2”. When I put in the “plus sign, +,” that means the Normal force is positive, whereas gravity is negative (down). “Normal” here means “perpendicular to the plane of the table,” or, up.
B. Hooke's Law, Energy, Work, Momentum
1. Hooke’s Law deals with springs (like in pens, in cars as shock absorbers, in toys like the Slinky...)
F = - k x, which means that the force, which is negative, pushes (or pulls) in the opposite direction to the external force. If I stretch a spring, it will recoil back to its original shape when I let go; if I compress a spring, it will push itself out to its original shape once I stop compressing it. The “k” is called the “spring constant.” A large k means a very strong spring, like in a shock absorber. A very small k means a very weak spring, like a Slinky. “x” means how far the spring is compressed in, or, stretched out.
In the Hooke's Law lab, we will use F = - k y instead, since we will be stretching a string downward in the negative y-direction. The force that we will apply will be a weight which will have the force of = m g. So, in the lab,
- k y = m g. We will measure “y” with a ruler, we will know the mass, and we know gravity.
2. Forms of Energy include, but are not restricted to:
· Heat
· Light
· Mechanical
· Acoustical, etc.
3. Kinetic energy (K.E.) is in motion = ½ mv2, the mass must have a speed or velocity. If it is not moving, NO K.E.
Potential energy (P.E.) is stored energy. For storing potential energy when working against the force of gravity, P.E. = mgh = (mass)(acceleration)(height above starting point).
An Example: take a 5-kg cat and carry him up a hill about 100 meters. You will have stored this much P.E. in the cat: mgh = (5kg)(- 9.8 m/s2)(100 m) ~ 5000 Joules.
If you then release (drop) the cat over the edge of a cliff that is 100 meters above where you started, 5000 Joules will be released and turn into K.E. as the cat is falling, until he impacts with the ground. The instant just before impact all the 5000 Joules have changed from P.E. to K.E. After impact, the energy then is transferred into heat (thermal energy), sound (acoustical energy), destruction (mechanical energy), and so forth.
4. The only good thing about energy is to use it to do work for us. However, nothing is 100% efficient, so the amount of work done divided by the available energy to do that work is a ratio: Work / Energy < 1, which means, less than 100%.
If I were to use a force, F, and push a mass, m, a distance, d, then the amount of work that I would do on that object would be the force times the distance moved, or F x d = energy, units 1.0 N-m == Joule
5. In chemistry, calories are used as the main concept of energy, and 4.186 calorie = 1 joule.
However, 1,000 calories, or, 1 kcal is what is called a “food calorie” or, a Calorie with a capital “C”. 1.0 Calorie = kcal.
The stuff below was NOT covered, but will be:
6. Momentum = energy of motion
p = m v
Dp = 0 in a closed system
VII Laboratory Exercise 5: Potential and Kinetic Energy
VIII HWK Assignment 2: 5-9 and do Problems 1, 3, 9, 13, 19, 25, 29, 31, and 39 on pp 140-143; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, and 65 on pp 177-184; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, and 53 on pp 210-213; and Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, and 53 on pp 244-248; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, and 53 on pp 289-292.due 8/12
IX Essay 2: Sir Isaac Newton, due 8/12
TUESDAY, AUGUST 10, 2010
I Introduction
II Logistics
III Return of tests, labs, papers; collection of overdue assignments
IV Running Grades
V Review of Lesson 4: Newton's Laws of Motion
A. Objects at rest, stay at rest; objects in motion stay in motion; UNLESS acted upon by an Fext.
B. F = m a à ties into the Universal Law of Gravity
C. Every force has an equal and opposite force, or, F1 = - F2.
D. Units of force are “Newtons”, kg m/s2. = N
F = ma
v = x/t
VI Lesson 5: Forces
A. The force of friction, Ff = mN = + mmg, which means the force of friction equals a number (m) that is called the “coefficient of friction” multiplied by the equal and opposite force to gravity, N, the Normal force; or N = mg, where m is the “mass” and g is the acceleration of gravity, “9.8 m/s2”. When I put in the “plus sign, +,” that means the Normal force is positive, whereas gravity is negative (down). “Normal” here means “perpendicular to the plane of the table,” or, up.
B. Hooke's Law, Energy, Work, Momentum
1. Hooke’s Law deals with springs (like in pens, in cars as shock absorbers, in toys like the Slinky...)
F = - k x, which means that the force, which is negative, pushes (or pulls) in the opposite direction to the external force. If I stretch a spring, it will recoil back to its original shape when I let go; if I compress a spring, it will push itself out to its original shape once I stop compressing it. The “k” is called the “spring constant.” A large k means a very strong spring, like in a shock absorber. A very small k means a very weak spring, like a Slinky. “x” means how far the spring is compressed in, or, stretched out.
In the Hooke's Law lab, we will use F = - k y instead, since we will be stretching a string downward in the negative y-direction. The force that we will apply will be a weight which will have the force of = m g. So, in the lab,
- k y = m g. We will measure “y” with a ruler, we will know the mass, and we know gravity.
2. Forms of Energy include, but are not restricted to:
· Heat
· Light
· Mechanical
· Acoustical, etc.
3. Kinetic energy (K.E.) is in motion = ½ mv2, the mass must have a speed or velocity. If it is not moving, NO K.E.
Potential energy (P.E.) is stored energy. For storing potential energy when working against the force of gravity, P.E. = mgh = (mass)(acceleration)(height above starting point).
An Example: take a 5-kg cat and carry him up a hill about 100 meters. You will have stored this much P.E. in the cat: mgh = (5kg)(- 9.8 m/s2)(100 m) ~ 5000 Joules.
If you then release (drop) the cat over the edge of a cliff that is 100 meters above where you started, 5000 Joules will be released and turn into K.E. as the cat is falling, until he impacts with the ground. The instant just before impact all the 5000 Joules have changed from P.E. to K.E. After impact, the energy then is transferred into heat (thermal energy), sound (acoustical energy), destruction (mechanical energy), and so forth.
4. The only good thing about energy is to use it to do work for us. However, nothing is 100% efficient, so the amount of work done divided by the available energy to do that work is a ratio: Work / Energy < 1, which means, less than 100%.
If I were to use a force, F, and push a mass, m, a distance, d, then the amount of work that I would do on that object would be the force times the distance moved, or F x d = energy, units 1.0 N-m == Joule
5. In chemistry, calories are used as the main concept of energy, and 4.186 calorie = 1 joule.
However, 1,000 calories, or, 1 kcal is what is called a “food calorie” or, a Calorie with a capital “C”. 1.0 Calorie = kcal.
The stuff below was NOT covered, but will be:
6. Momentum = energy of motion
p = m v
Dp = 0 in a closed system
VII Laboratory Exercise 5: Potential and Kinetic Energy
VIII HWK Assignment 2: 5-9 and do Problems 1, 3, 9, 13, 19, 25, 29, 31, and 39 on pp 140-143; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, and 65 on pp 177-184; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, and 53 on pp 210-213; and Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, and 53 on pp 244-248; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, and 53 on pp 289-292.due 8/12
IX Essay 2: Sir Isaac Newton, due 8/12
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