Martin Teachworth
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Teacher Assistance And Explanation
Martin Teachworth
La Jolla High School
454 - 3081
Do Bowling Ball Lab One first. Determine the average velocity using V = d / t (velocity =
distance divided by time) The velocity equals the meters traveled divided by the time recorded. The
velocity has the units of meters/second (m/s).
Do Bowling Ball Lab Two next. The slope of the graph should be a constant. The slope will be
equal to the average velocity. Determine the average velocity using V = d / t (velocity = distance divided
by time) The velocity = the meters divided by the time recorded. The velocity has the units of
meters/second (m/s).
Keep the release points for all students release is the very top of the ramp. Life will be much
simpler if all groups release the ball from the same point. The velocity determined at this point should be
recorded and kept for the next lab.
An average velocity is the velocity over a long period of travel. An instantaneous velocity is the
velocity at any instant of time. A speedometer shows the instantaneous velocity. For example, a trip to
Disneyland may take 3 hours to go 120 miles. The average velocity is 40 miles/hour, but the velocity varies
from 0 to the fastest velocity (60, 70, 90? mph) traveled during the trip.
To measure the instantaneous velocity using a stop watch and meter tape, a very short distance
then the time it took the ball to travel that distance would have to be measured. The problem with this is the
reaction time of the person measuring the time. The reaction time of a person is at best about .1 seconds.
Anything measured by humans must take this into consideration.
Do Bowling Ball Lab 3 after the first two. Take the ramp and table out to a grassy or sandy area.
Release the ball from the top point on the ramp that all students were to record the velocity from the second
golf ball lab.
Students record the distance the ball rolls from the base of the ramp. Set a tape measure next to the
path the balls take, to allow students to quickly and easily measure then record the distance. The rolling of
balls for the lab should take no more than 15 to 20 minutes. As soon as the ball is rolled, have students
measure and record then get into line to roll the ball again.
The instantaneous velocity at the base of the ramp is the average velocity recorded from the
second lab. The assumption is made that the ball's acceleration (a negative acceleration) is constant over the
entire length of travel. While this may not be entirely correct it allows the motion equations assuming a
constant acceleration to be used.
Part Two
2
2
To determine the acceleration the equation, V = V + 2 a x is used. The value of V is zero meters per
f
o
f
second. This is the final velocity of the ball after finishing rolling. The value of V is the velocity recorded
o
from the first lab. This is the velocity of the ball when first rolling on the grass. The value of x is the
distance the ball rolls on the grass.
The final form of the equation after the algebra has been done will be:
2
2
V
- V
f
o
a = ------------2x
Since V is zero, the equation changes to:
f
2
- V
o
a = ------------2x
Part Three
The negative acceleration just means that the ball is slowed until it stops.
- V
o
a = ------------t
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Martin Teachworth
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BOWLING BALL AVERAGE VELOCITY
PURPOSE - To determine average velocities
HYPOTHESIS - NOT NEEDED FOR THIS LAB
EQUIPMENT - Ramp, bowling ball, meter stick, stop watch, hallway
PROCEDURE
1. Mark off a 5.0 meter distance on the floor from the base of the ramp.
2. Use the same height each time the ball is released.
3. Release the bowling ball.
4. Start the timer when the ball crosses the first mark.
5. Stop the timer when the ball crosses the second mark.
6. Complete the data table.
RESULTS
RELEASE FROM POSITION 12 ON THE RAMP
DISTANCE TRAVELED
(METERS)
5.0
5.0
5.0
5.0
5.0
5.0
AVERAGE
TOTAL TIME
(SECONDS)
AVERAGE VELOCITY (M/S)
Use the DUFAS method to solve for the AVERAGE VELOCITY
CONCLUSION
1. What formula was used to determine the average velocity of the bowling ball?
2. Explain the difference between an average velocity and an instantaneous velocity.
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Martin Teachworth
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Bowling Ball Average Velocity
And Graphical Analysis
PURPOSE - To determine average velocities using graphical analysis
EQUIPMENT - Ramp, bowling ball, meter stick, stop watch, hallway
PROCEDURE
1. Mark off different distances on the floor from the base of the ramp.
2. Use the same height each time the ball is released.
3. Release the bowling ball.
4. Start the timer when the ball crosses the first mark.
5. Stop the timer when the ball crosses the second mark.
6. Complete the data table.
RESULTS
RELEASE FROM POSITION 12 ON THE RAMP
DISTANCE
TIME
TIME
TRAVELED
(SECONDS)
(SECONDS)
(METERS)
Average
Time
(SECONDS)
AVERAGE VELOCITY (M/S)
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Graphical Analysis
Make a graph - Remember all the parts of a graph must be present for full credit.
Independent variable (Average Time)
Dependent variable (Distance Traveled)
Determine the slope (with units) and correlation coefficient
Percent Difference = 100 ( Slope – Average Velocity)
Slope
CONCLUSION
1. What formula was used to determine the average velocity of the bowling ball?
2. Explain the difference between an average velocity and an instantaneous velocity.
3. What do the slope units represent?
4. Make a sketch of what the graph would look like if the ball were rolling across a rough floor with
lots of friction.
5. Explain why the graph would have the shape drawn to answer question 4.
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Martin Teachworth
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BOWLING BALL LAB 3
ACCELERATION
PURPOSE - To determine average acceleration
EQUIPMENT - Ramp, books or VERY low table, golf ball, meter stick, stop watch, ROUGH surface
area (grasS)
PROCEDURE
1. Release the ball from a height for which the velocity at the base is known (use data from a previous
lab). Be sure the testing area is as flat as possible.
2. Time how long it takes the ball to roll each distance.
3. Measure the time for every meter until the ball stops rolling.
4. Determine the total distance and the total time the ball rolled before stopping.
5. Complete the data table.
RESULTS
INITIAL VELOCITY AT THE BASE OF THE RAMP ______ m/s (From a previous lab)
FINAL VELOCITY AT END OF ROLLING
Meters
(m)
Time
(s)
__________ m/s
Distance and Time Measurements
Time
Time
Time
Time
(s)
(s)
(s)
(s)
Average
Time
(s)
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
Continue data table until the ball comes to a complete stop.
TOTAL DISTANCE AND TIME THE BALL
ROLLED FROM THE BASE OF THE RAMP
TOTAL
TRIAL
TRIAL
TRIAL
TRIAL
TRIAL
ONE
TWO
THREE
FOUR
FIVE
DISTANCE
ROLLED
TIME
ROLLED
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Average
Martin Teachworth
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ANALYZED DATA
Part One
Make a graph (on graph paper) of the Time (x axis) versus the Distance (y axis). Plot the points then
draw a line through the center of the points. The line should curve and not be a straight line.
Use the computer to plot the graph. Find and draw the regression line. Do not use a simple curve fit,
use a polynomial curve fit. Be sure to copy down the equation and the correlation coefficient (R value).
Part Two
DETERMINE THE AVERAGE ACCELERATION USING THE TOTAL DISTANCE ROLLED OF
THE BALL AFTER IT LEAVES THE RAMP
V f2 = V o 2 + 2 a d
so
a = ----------------
Vf2 = the final velocity squared (when the ball stopped rolling)
It is zero meters per second.
2
Vo = the original velocity squared
(how fast the ball is rolling at the bottom of the ramp)
Use this equation to find the average acceleration for the trip.
a= -
Velocity at the bottom of the ramp squared
----------------------------------------------2 (Maximum Distance Rolled)
AVERAGE ACCELERATION ______ m/s
2
(This will be a negative acceleration or a deceleration)
Part Three
DETERMINE THE AVERAGE ACCELERATION USING THE TOTAL TIME ROLLED OF THE
BALL AFTER IT LEAVES THE RAMP
Vf = Vo + a t
a= -
Velocity at the bottom of the ramp
----------------------------------------------Maximum Time Rolled
CONCLUSION
1. What was the velocity of the bowling ball at the base of the ramp?
2. What formula was used to determine the average ACCELERATION of the bowling ball?
3. Why is the average acceleration on the outside area a negative number?
4. Explain why the average of the data points on the graph is not a straight line.
5. How could the graph be used to determine the speed of the ball at any point of travel?
6. Explain the difference between an average and an instantaneous velocity.
7. Explain how to recognize acceleration on a displacement versus time graph.
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