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The current land-speed record was set in the Black Rock Desert of Nevada in 1997 by the jet-powered car Thrust SSC. The car's speed was 1222 km//h in one direction and 1233 km//h in the opposite direction. Both speeds exceeded the speed of sound at that location (1207 km/h). Setting the land-speed record was obviously very dangerous for many reasons. One of them had to do with the car's wheels. Approximate each wheel on the car Thrust SSC as a disk of uniform thickness and mass M = 170 kg and assume smooth rolling. When the car's speed was 1233 km/h, what was the kinetic energy of each wheel? |
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Answer» Solution :KEY IDEAS Equation 11-5 gives the kinetic energy of a rolling object, but we need three ideas to use it: (1) When we speak of the speed of a rolling object, we always mean the speed of the center of MASS, so here `v_("com") = 1233 km//h = 342.5 m//s`. (2) Equation 11-5 requires the angular speed `omega` of the rolling object, which we can relate to `v_("com")` with Eq. 11-2, writing `omega= v_("com")/R`, where R is the wheel.s radius. (3) Equation 11-5 also requires the rotational inertia `I_("com")` of the object about its center of mass. From Table 10-2c, we find that, for a uniform disk, `I_("com") (1/2)MR^(2)`. Calculations: Now Eq. 11-5 gives us `K= (1)/(2)I_("com")omega^(2)+ (1)/(2)Mv_("com")^(2)` `((1)/(2))((1)/(2)Mr^(2))((v_("com"))/(R))^(2)+ (1)/(2)Mv_("com")^(2)` `= (3)/(4)(170kg)(342.5m//s)^(2)` `= 1.50 xx 10^(7)J` (Note: The wheel.s radius R cancels out of the calculation.) Reasoning: This ANSWER gives one measure of the dan ger when the land-speed record was set by Thrust SSC: The kinetic energy of each (cast aluminum) wheel on the car was huge, almost as MUCH as the kinetic energy (`2.1 xx 10^(7) J`) of the spinning steel disk that exploded in Sample Problem 10.8. Had a wheel hit any hard obstacle along the car.s path, the wheel would have exploded the WAY the steel disk did, with the car and driver moving faster than sound! |
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