Mountain Bike Lab
Supplies
- 1 Bicycle Training Stand
- 1 90 lbs weight set
- 1 70 lbs weight set
- 1 50 lbs weight set
- 1 Bicycle
- Colored tape
- 1 Fish scale
Objectives
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Students will describe how the gears on a mountain bike affect mechanical
advantage and torque.
Students will determine the spring constant and damping coefficient for the
shocks on the mountain bike.
Students will understand how objects change their motion when a net force is
applied and that laws of motion can be used to calculate precisely the effects of
forces on the motion of objects (NSC Standard B).
Students will conduct a scientific investigation (NSC Standard A).
Students will use technology and mathematics to improve investigations and
communications (NSC Standard A).
Students will increasing their technological understanding and recognize that
technological design is driven by the desire to meet human needs and solve
human problems (NSC Standard E).
Concepts
Torque
 Is the tendency of a force to rotate an object about an axis
 The greater the distance from the axis of rotation the greater the torque will be
 Torque = force * length of the lever arm
Gears
 Gears trains can be used to increase torque and decrease speed, or to increase speed
and decrease torque
 A small gear driving a large gear will create more torque
 A large gear driving a small gear will create more speed
 Torque of the gears is governed by equation 3 on the equation sheet.
 Speed of the gears is governed by the gear ratio
o (Speed A * Number of teeth A) = (Speed B * Number of teeth B)
Spring constant
 The force exerted by the spring is directly related to the displacement times the
spring constant
 Linear materials use Hooke’s law of F=k*x
o F = force
o k = spring constant
o x = distance the spring has been compressed or stretched
 Units are force per unit length (SI is Newton meters)
Damping Coefficient, c
 Damping Coefficient determines how damped (responsive) a shock is or how long a
shock will oscillate if at all
 Units of mass per unit time
 System can be (Fig 3)
o Underdamped ( < 1) Lots of oscillations
 Ex. Rubber band
o Critically damped ( = 1) No oscillations, but moves quickly
 Ex. Car shocks
o Overdamped ( > 1) No oscillations, but moves slowly
 Ex. Door damper
 Equation relating spring constant and mass to damping coefficient
o c=*2*(k*m)(1/2)
o k = spring constant, m = mass
Part 1: Mechanical Advantage and Torque
1. Count the number of teeth on the largest and the smallest chain ring of the front
(driver) gears. Use the colored tape to help you keep track of where to start and
stop counting. Enter these values in the tables on the attached sheet.
2. Count the number of teeth for at least three of the gears in the back (cassette) and
record these values in the tables below. Try counting for the biggest, smallest, and
a medium gear. When you are finished, each blank in the first two columns of
each table should be filled in, giving you six gear combinations.
3. Measure the length (l) of the arm of the pedal. Measure from the center of the
crank to the center of the pedal. Record this length below. Later, you will need
this value to determine the torque using Equation 2 from your Equation Sheet.
l = __________________
4. Attach the fish scale to a pedal and pull on it at a 90 degree angle from the pedal
arm. Use the scale to determine how much mass is required to start the wheel
turning. Make sure to record in kilograms (kg). Repeat this process for each
combination of gears. Use equation 4 to convert the mass to force and record the
necessary force for each combination in the tables below. For simplification,
assume the acceleration is gravity.
5. Calculate the mechanical advantage for each of the gear combinations using
Equation 1 from your Equation Sheet. Record each mechanical advantage in the
tables.
6. Using the length (l) and the force you recorded in the previous step, calculate the
experimental torque for each combination of gears using Equation 2 from your
Equation Sheet. Enter these values in the tables. Make sure to have the correct
units i.e. keep cm, and meters straight.
7. Using the data that you have recorded in your table and Equation 1 from your
Equation Sheet, find the output torque of the bicycle. Record this information in
the tables.
Part 1 Data Tables
Number of Teeth
Back
Big Front Gear
Gear
Mechanical
Advantage
Force
Experimental
Torque
Output Torque
Number of Teeth
Small Front
Back
Gear
Gear
Mechanical
Advantage
Force
Experimental
Torque
Output Torque
Part 2: Spring Constant and Damping Coefficient
1. Position your yardstick parallel to the bicycle shock and measure the height of the
upper edge of the shock. Record this uncompressed length below as xlong.
xlong = _________________________
2. Add 50 lbs, 70 lbs, or 90 lbs of weight to the bicycle by loading equal amounts on
each side of the handle bars (two 25 lb weights = 50 lbs, etc). Make sure to put
both weights on and take both weights off at the same time to prevent from
tipping the bike.
3. Now that you have weighted the bicycle, use your yardstick to measure the height
of the shock as you did in step 1. Record this compressed length, xshort, in the
appropriate space below. Make sure to have the correct units i.e. keep cm, and
meters straight.
22.68 kg xshort = ___________________________________
31.75 kg xshort = ___________________________________
40.82 kg xshort = ___________________________________
4. Determine the force that you applied to the shock using the equation 4. Record the
force in the appropriate space below.
22.68 kg F =___________________________________
31.75 kg F =___________________________________
40.82 kg F =___________________________________
5. Use Equation 5 from your Equation Sheet and the data you have collected so far
to determine the spring constant (k) for the bike. Record this value in the
appropriate space below.
22.68 kg
k = ___________________________________
31.75 kg
k = ___________________________________
40.82 kg
k = ___________________________________
6. Repeat steps 2-5 with all 3 different sets of weight, filling in your lab sheet as you
go.
7. Assume that the damping ratio ( is equal to 1 (the system is critically damped).
Use Equation 6 from your Equation Sheet to find the damping coefficient c for the
bike. Record this information in the appropriate space below.
22.68 kg
c = ___________________________________
31.75 kg
c = ___________________________________
40.82 kg
c = ___________________________________
8. Now find the average k and c values for the bicycle and record these values
below.
Average k = ___________________________________
Average c = ___________________________________
Questions
1. How are the output and experimental torques related?
2. What was the largest mechanical advantage you could achieve with the bike?
How would this affect the resistance of your pedaling and the wheel speed?
3. What was the smallest mechanical advantage? How would this affect the
resistance of your pedaling and the wheel speed?
4. What would happen if you increased k on the bike?
5. What would happen if you increased c on the bike?
6. How could bicycle manufacturers use what you have learned through this lab?
Equation Sheet
eq 1
N1
MA
MA = mechanical advantage
N2
N1 = number of teeth on driven gear (back gear)
N2
F l
eq 2
T
eq 3
N1
T1
N2
T2
eq 4
F
= number of teeth on driver gear (front gear)
T = torque (N*m), F = Force (N) , l=length (m)
T1 = output torque (N*m)
T2 = experimental torque applied (N*m)
N1 = number of teeth on gear 1
m a
m = mass (kg)
N2
= number of teeth on gear 2
a = acceleration (gravity)
a
9.807
m
s
eq 5
F
k x
F=force (N), k=spring constant
eq 6
c
2 k m
 = damping ratio
eq 7
2
r1
N1
T1
1
r2
N2
T2
k=spring constant
master equation
x
2
xlong  xshort
m = mass (kg)
(m)
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