### Assignment Instructions/ Description

Image transcription textAt the instant you step on the pedal (assuming we step straight down on the pedal, where 0=90 ), your weight (F1)

acts at a distance |1, creating a torque = F1/1. The torques on the pedal and the front sprocket system are equal to

one another, such that:

F1 11 = F2 12

[2]

The force exerted on the chain, F2 by the front sprocket is equal to the force exerted by the chain on the rear

sprocket. The force is transmitted directly, so

F2 = F3

[3]

The torque from the rear sprocket on the axle is equal to the torque on the wheel from the road.

F3 13 = F4 14

[4]

By measuring the lever arms, and starting with F1, the weight of the rider, we can calculate the force the tire

exerts on the road.

PROCEDURE

1. Enter some basic data about your bike and yourself in Table 1. Be sure to convert your weight into Newtons.

2. Measure the lever arms involved when bike is in low (1st) gear. This should be when the chain is on the

smallest front sprocket (aka chainring) and largest rear sprocket. Enter your data in Table 2. Take care in

measuring the lever arm lengths to the center of rotation of the arm

3 .

Compute the force the tire exerts against the road in low gear. Enter this value in Table 2. Show your work in

the space following Table 2.

4.

Repeat Steps 2 & 3 for when the bike is in high (10th, 18th, 21st ?) gear. This will be when the chain is in the

largest front sprocket and the smallest rear sprocket. Enter these values in Table 2.

5. Compute the force the tire exerts against the road in high gear. Enter this value in Table 2.

6. Repeat Steps 2 & 3 for when the bike is in approximately middle gear. This will be when the chain is in the

middle front sprocket (if there is one) and the middle rear sprocket. Enter these values in Table 2.

7. Compute the force the tire exerts against the road in middle gear. Enter this value in Table 2.

** You ONLY need to submit pages 4-7 for the assignment **... Show moreImage transcription textAPPLIED TO THE BIKE:

When pedaling a bike, the tire pushes against the road and the road pushes against the tire (Newton's 3'd Law)

To compute the force the tire exerts against the road (and therefore the road exerts back against the tire) when

you push against the pedal (as in Figure 3), we must analyze the many lever arms on the bike (see your bike). To

simplify, we can use the following variables for the lever arms:

1 = lever arm for front pedal (i.e. 'length' of pedal crank arm)

12 = lever arm for front sprocket (i.e. 'radius' of front gear used)

13 = lever arm for rear sprocket (i.e. 'radius' of rear gear used)

r4 = lever arm for rear wheel (i.e. the 'radius' of the rear wheel)

front

(driving)

rear

sprocket

(driven)

sprocket

drive

wheel

L1

ra

diameter

13

r2

And the following variables for the forces involved:

F1 = your weight

F2 = force exerted on the chain

F3 = force exerted by the chain

F4 = force of the tire against the road

F1

front

(driving)

rear

sprocket

F3

(driven)

sprocket

drive

wheel

diameter

F2

O

F4... Show moreImage transcription textLAB EXERCISE: TORQUE WITH BIKES

EQUIPMENT

Meterstick or measuring device

Multi-speed Bike with multiple gears (front & back) - if you don't have one, try Walmart, or a bike

store, or a friend. You only need access for 10 minutes to make some measurements.

OBJECTIVE

To investigate and calculate torque and mechanical advantages of the gears on a bicycle.

BACKGROUND

When a simple lever is balanced (like a see-saw balanced 'horizontally'), the sum of the torques on one side of

the fulcrum (or point of rotation) is equal and opposite to the sum of the torques on the other side. In other words,

everything attempting to rotate the lever clockwise is balanced, or counteracted, by everything trying to rotate the

lever counterclockwise. This lever principle or torque equation can be summarized as:

F1 d1 = F2 d2

[1 ]

We can solve for any variable in the above equation if the other three variables are known. We will use this idea

in the next lab exercise, when we investigate the two conditions necessary for equilibrium of a rigid body. For

now, know that levers are usually designed with a specific purpose in mind. Although levers can't reduce the

amount of work to be done, they can make it easier. Think of how torque wrenches, tire levers or pipe wrenches

make work easier. Mechanical Advantage (MA) is a measure of this reduction in effort.

Mechanical Advantage can be useful in two different ways. A smaller effort force positioned farther from the

fulcrum of a lever can overcome a larger resistance force. The price paid is moving the smaller force through a

larger distance. Figure 1 shows a lever, which results in such a gain in force, more commonly known as "torque",

hence, a "torque wrench". The torque is calculated by T = F d sin 0, where F = force, d = lever or torque arm

length, and 0 = angle between Force and lever arm.

Lever Arm

Examples: your hand pulling

up on the wrench, or your foot

FORCE

pushing down on a bike pedal.

The lever arm is the distance

between the rotation point and

the point the force is applied.

Figure 1... Show moreImage transcription textBike Type

# of speeds

Weight of Rider (N)

TABLE 1 - BIKE & RIDER INFORMATION

Gear

h1(m)

rz (m)

r's (m)

ra (m)

Froad (N)

Low

High

Middle

TABLE 2 - LEVER ARMS AND FORCE

SHOW THE CALCULUATIONS FOR ONE GEAR SET (LOW, HIGH, MIDDLE) HERE FOR STEP #3:

Calculating the Force on the road... Show moreï¿½