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Situation: You have always been fascinated with SoapBox Derby. So you decided to

ID: 1483167 • Letter: S

Question

Situation: You have always been fascinated with SoapBox Derby. So you decided to join a club that designs SoapBox Derby cars. You are put in charge to design one of the cars that the club will enter into the annual downhill derby. As you are working on the car, you have the choice of putting one of the following wheels on the car: solid wheels, bicycle wheels with thin spokes, or solid spherical wheels. Which wheels will make the race car go the fastest? So you start to experiment with the various types of wheels down an incline to see which reaches the bottom the fastest. Suppose that a wheel of radius a and mass M starts from rest at the top with potential energy PE= Mgh and reaches the bottom with angular speed and (linear) velocity v_a conservation of energy) the wheel's initial potential energy has been transformed Then (by =1Miand rotational into a sum KE, + KE oroftranslational kinetic energy KE 2 kinetic energy KE,,-2402 =

Explanation / Answer

here,

moment of inertia of solid wheels , I1 = 0.5 * m * a^2

moment of inertia of bicycl wheels , I2= m*a^2

moment of inertia of solid sphereical wheels , I3 = 0.4 * m * a^2

KEr + KEt = PE

for same potential energy

for the radius of gyration be minimum , the kinetic energy is maximum

therfore , solid sphereical wheel make the car go fastest

b)

for uniform solid disk

I0 = 0.5 * m * a^2

KEr + KEt = PE

0.5 * 0.5 * m * a^2 * ( v/a)^2 + 0.5 * m * v^2 = m * g * h

0.75 * v^2 = 9.8 * h

v = 3.61 * sqrt(h)

the speed at the bottom of incline is 3.61 * sqrt(h)