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## 4.1 Bicycles

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**Clicker question**Which vehicle is most stable? (B) Bicycle (A) tricycle (C) This chopper bike (D) An SUV**Tricycle**But both the SUV and tricycle have major problems turning! A bike always flops over when it’s not moving… …but a regular bike is very stable when turning.**Statically stable**Dynamically unstable Statically unstable Dynamically stable Statically unstable Dynamically stable? Statically stable Dynamically unstable**A tricycle is statically stable**It’s base of support is a triangle defined by the points of contact (tires and ground). c-o-m**Static stability is determined by**1. base of support (polygon formed by ground contact points) 2. center of gravity (effective point at which gravity acts) Static stability occurs when the center of gravity is above the base of support Vehicle’s Static Stability Stability demos**If we go too far…**Energy becomes smaller in this direction mgh mgh Gravitational potential energy increases Tips over to a new stable equilibrium Stable equilibrium means that gravitational potential energy rises when the object is tipped**You can also understand this using torque**Tricycle: statically stable Bicycle: statically unstable**Tricycles**have 3 contact points are statically stable and hard to tip over Bicycles have only 2 contact points are statically unstable and hard to keep upright Base of support requires at least three contact points: Stationary Vehicles:**Why does an SUV roll?**r Ffriction Too much torque around center of mass! Let’s think about forces and acceleration.**SUVs and tricycles are dynamically unstable because the**total force does not point to the center-of-mass. There’s a torque around c-o-m from the friction force! Support force Total force**Sports car**• c-o-m low • Lever arm small torque • VW van / SUV • c-o-m high • Lever arm big**Clicker question**Why does Lance ride a bike and not a tricycle? (What makes a bike dynamically stable?) (A) A cyclist can lean on a bike and change the torque around his center of mass. (B) The pedals on a bike are connected to the rear wheel (in contrast to the front wheel on a tricycle), making it possible for the cyclist’s feet to work independently of the bike’s motion. (C) A bicycle has brakes, so the cyclist can change speed quickly.**Leaning during turns allows total force to point towards**center of gravity, so no net torques!**Dynamic effects can aid a vehicle’s stability**- by shifting base of support to under the center of gravity (meter stick) • by dynamically stabilizing an equilibrium, i.e., reduce net torques (bicycle) And, can make a statically unstable vehicle dynamically stable Vehicle’s Dynamic Stability**A bicycle has some special features which make it incredibly**dynamically stable A bicycle steers automatically! • Acts like a gyroscopic • “Trail” – the shape of the fork “Trail” is the dominant effect at low speed**Chopper bike**Trail – the shape of the fork One of these is not like the other. The wheel much touch the ground “behind” the steering axis for the bike to steer properly.**Gyroscope**Gyroscope, suitcase**Gearing**Gears are another important feature of bicycles (and cars!) not related to stability The pennyfarthing was designed to get mechanical advantage from gearing.**Gearing on a pennyfarthing:**the rider turns her feet through less distance than the wheel travels Going to the top of a hill: she does the same amount of work, so more force is required to turn the pedals (compared with a smaller front wheel) This is like a “high” gear**Gears allow you to exchange force for distance or distance**for force in doing work. • On steep hills, you use a gear that requires your feet to move a large distance in exchange for smaller force on the pedals. • On flat surfaces, you use a gear that requires your feet to push hard in exchange for a larger distance traveled by the rear wheel. Mechanical Advantage**Gears**Hence, the invention of the indirect drive