Phys151_PPLNine.F12[1]

# Just as before consider a 2nd example you apply a

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Just as before! Consider a 2nd Example. You apply a constant force of 20 N on a mass of 10 kg moving it 4.0 m. What is its speed at the end of this motion? Newton’s Law:F = m.a tells you the constant acceleration a = 20 / 10 = 2.0 m/s 2 . (a is not always 10 m/s 2 !) d = 4.0 m Time of travel is yielded by d = 1/2.a.t 2 .

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Work-Energy Theorem so 4.0 = 1/2.2.t 2 giving t = 2.0 s and therefore v = a t = 2 x 2 = 4.0 m/s Let’s use Work-Energy to solve the problem. Work = F.d = 20 x 4 = 80 J which is converted to KE (no GPE here since the surface is flat) so KE = 1/2.m.v 2 = 1/2.10.v 2 = 80 so that v = 4.0 m/s, just as before! This concept in Physics is called the Work-Energy Theorem The total work done on an object is its change in kinetic energy : W = KE Familiarity with the theorem allows us to understand Roller Coasters: E.g. why we move faster at the dips! Where we also feel lighter !
Work-Energy Theorem II Back to the 20 kg suitcase being dropped. The only force “working” on the suitcase is gravity. When the suitcase falls 1 m, gravity does 20.10.1 = 200 J of work. This is realized as a change of the kinetic energy of the suitcase. Work done by all forces = KE f - KE i so that W = 1/2.20.v f 2 - 0 and therefore, • 200 = 1/2.20. v f 2 And this gives the same answer as before!

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Power For the rollercoaster above, where will I move fastest? Power is defined as the rate at which work-energy is converted from one form into another . P = Work / t If a 150-lb man (lb is a weight measure) climbs up a ladder so that he is 5 ft above the floor and it takes him 3 seconds to do so, then he has increased his gravitational potential energy by 150 x 5 = 750 ft. lb. His power “rating” is 750/(3) ft.lb/s = 750/(3x550) = 5/11 hp. (since 550 ft.lb/s = 1 hp ) A B C D E
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