Bike 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 roadLAB 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 1APPLIED 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 F4At 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 **