Investigating the Mechanical Advantage of a Bicycle

Investigating the Mechanical Advantage of a Bicycle
Name: ______________________________________
(____/5 K/U, ____/7 T/I, ____/10 APP, ____/5 COM)
Introduction:
When you ride a bicycle on level ground, the gears increase or decrease the force that you need to exert on the
pedals to keep the bike moving. This change of force results in faster or slower speeds. The mechanical advantage
(MA) is the number of times the effort force (the force from your legs) is multiplied by the machine. Mechanical
advantage decreases or increases with the changing of the gears. The speed advantage (SA) is the number of
times that the machine multiplies the speed at which the
effort force is applied. If a bicycle multiplies the force of your legs by two, the speed is reduced by one-half.
Purpose:
In this lab, you will:
 determine the mechanical and speed advantages of a multi-gear bicycle.
 describe the functions of the gears on a ten-speed bicycle.
Materials:
multi-gear bicycle
string
block of wood
Newton spring scales
measuring tape
masking tape
metre stick/ruler
Procedure (Part A):
1. Place the block of wood under the bottom bracket of the frame. Have your lab partner steady the bicycle
by holding the seat and the handle bars. Now the rear wheel can turn freely when the pedals are turned.
2. Turn the pedals with one of your hands to make the rear wheel turn. While the wheel is turning, shift the
gears so that the bicycle is in first gear. While turning the pedal at a constant rate, slowly shift through the
ten gears. CAUTION: Do not shift gears when the rear wheel is not turning. Avoid placing your hand near
the rear wheel, drive chain, or gears. Observe the speed of the rear wheel as you shift through the gears.
Observe how the chain moves across the gears when you shift.
3. Remove the bicycle from the block of wood and lay it on its side.
4. Count the number of teeth on the front gear and rear gear for each combination of gears. Record these
values in the table.
Look at the bicycle gears shown in the diagram. If you count
number of teeth in the two gears, you will find that the front
has 52 teeth and the rear gear has 34. The mechanical
advantage of this combination of gears can be calculated by
the following equation.
MA 
the
gear
using
number of teeth on rear gear
number of teeth on front gear
For the gears shown, the mechanical advantage is
34
or 0.65
52
Calculate the mechanical advantage for each combination of your gears listed in the table. Record these values in
the Data Table.
Data Observations: (5 K/U)
Teeth on Front Gear
Teeth on Rear Gear
Mechanical Advantage (MA)
Questions and Conclusions
1. Explain how the use of 3 large gears and 7 small gears produces 21 different mechanical advantages.
(2 APP)
2. What gear combination produced the greatest mechanical advantage? (1 APP)
3. Which gear combination do you think is the best for hill-climbing? (2 APP)
4. Which gear combination do you think is the best for racing on a level track? (2 APP)
Procedure (Part B):
1. Using the meter stick measure the outside diameter of the rear tire if possible to the nearest 0.1 cm. To
get the radius of the tire, divide the diameter by two. Record your answer in the data collection and
analysis section.
2. Measure the diameter of the smallest rear gear. Measure the bottom of the tooth on one side of the gear
to the bottom of the tooth on the other. Divide by two to get the radius. Record this and the data
collection and analysis section.
3. Locate the center of the pedal crank and the center of the bolt that connects the pedal to the crank.
Measure the distance between these points [the length of the pedal crank]. Recorded it in the data
collection and analysis section.
4. Place a small piece of tape on the side of the rear wheel and another piece of tape on the floor. Set the
bicycle operate on the floor so that the tape on the wheel is directly above the tape on the floor.
5. While turning the pedal by hand, move the bicycle forward until the pedal crank is gone around one full
turn. Use one of the frame tubes on the bicycle for reference. Start with the paddle lined up with the
tube. Stop when it is gone one full-term and is lined up again. Be sure you have gone as close to one turn
as possible. Place another piece of tape on the floor where the rear tire now makes contact with the floor.
6. Measure the resistance distance, which is the distance the bicycle travel between the two pieces of tape
on the floor. Record your result in the data collection and analysis section.
7. Repeat steps 5 and 6 two more times. Calculate and record the average resistance distance from the
three trials.
8. Calculate the effort distance, which for one turn of the paddle is the circumference of the circle with the
radius equal to the length of the pedal crank. To do this, multiply the length of the crank by 2 (6.28).
Record this in the data collection and analysis section.
9. Calculate the overall mechanical advantage of the bicycle [in that particular gear] by dividing the effort
distance by the average resistance distance from step seven.
Extension: Take measurements and calculate the mechanical advantage
for the largest gear ratio and the smallest gear ratio as
shown by your teacher.
Data Collection and Analysis: (5 COM)
Outside Radius of rear tire
Radius of smallest rear gear
Length of pedal crank
Resistance distance (Trial #1)
Resistance distance (Trial #2)
Resistance distance (Trial #3)
Resistance distance (average)
Effort Distance
Overall Mechanical Advantage
cm
cm
cm
cm
cm
cm
cm
cm
cm
Extension:
Load Force (Lowest gear)
Effort Force (Lowest gear)
N
N
MA (Lowest gear)
Load Force (Highest gear)
Effort Force (Highest gear)
N
N
MA (Highest gear)
Concluding Questions:
1. Think of the smallest rear gear of your bicycle as the axle, and the rear tire as the wheel. If you turn the
axle so that it internally rotates the wheel, what mechanical advantage do they have to gather? What
does it mean that the mechanical advantage you calculated is less than one? (2 T/I, 2 APP)
2. What is the overall mechanical advantage of the bicycle? Is a greater or less than the bank mechanical
advantage of the rear wheel combined with the rear gear? (3 T/I)
3. From your experience [assuming you have written a bicycle], in which gear is it easier to paddle, the
largest rear gear or the smallest rear gear? (1 APP)
4. You probably did not get exactly the same resistance distance for all three trials. Describe at least two
possible sources of in accuracy. (2 T/I)