MET410 - U3 - Review Assignment.docx - Unit 3 Review 12-1 A...

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Unit 3 Review 12-1 A high-speed escalator travels at 180 ft/min. What is the absolute velocity of a person running at 700 ft/min (a) in the same direction as the escalator’s motion and (b) in a direction opposite to that of the escalator’s motion? a) V A = V B + V B / A = 180 ft min + 700 ft min = 880 ft min b) V A = V B + V B A = 180 ft min 700 ft min =− 520 ft min 12-10 a) ω B = ( 400 rev min )( 2 π rad rev )( min 60 sec ) = 41.89 rad sec v B = ( r AB )( ω B ) = ( 175 mm ) ( 1 m 1000 mm )( 41.89 rad sec ) = 7.33 m sec When θ=0, point C has no angular velocity because it is horizontally locked, so the velocity is v B = v C + v B / C = 7.3304 m s + 0 = 7.3304 m s ( positive horizontal ) b) When θ=90 velocity at B is still the same as our prior calculation
v B = 7.3304 m s sin a = 75 10 3 .5 →a = sin 1 ( .15 ) = 8.63 ° ϕ = 180 ° 90 ° 8.63 ° = 81.37 ° v C = v B cot ϕ = 7.334 m s cot ( 81.37 ° ) = 1.112 m s 12-12 To get the measure of angle B for the vector triangle here, we use α = tan 1

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