{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# om4 - hernandez(ejh742 oldmidterm 03 Turner(58120 This...

This preview shows pages 1–3. Sign up to view the full content.

hernandez (ejh742) – oldmidterm 03 – Turner – (58120) 1 This print-out should have 24 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A rotating bicycle wheel has an angular speed of 40 / s at 3 . 6 s and a constant angular acceleration of 37 / s 2 . With the center of the wheel at the origin, the valve stem is on the positive x -axis (horizontal) at t 0 = 1 . 3 s. Through what angle has the valve stem turned between 1 . 3 s and 7 . 1 s? Correct answer: 360 . 76 . Explanation: Let : ω 1 = 40 / s , t 1 = 3 . 6 s , α = 37 / s 2 , θ 0 = 0 , t 0 = 1 . 3 s , and t = 7 . 1 s . The initial angular velocity can be deter- mined from ω 1 = ω 0 + α ( t 1 t 0 ) ω 0 = ω 1 α ( t 1 t 0 ) = 40 / s (37 / s 2 ) (3 . 6 s 1 . 3 s) = 45 . 1 / s . This θ 2 = ω 0 ( t 2 t 0 ) + 1 2 α ( t 2 t 0 ) 2 = ( 45 . 1 / s) (7 . 1 s 1 . 3 s) + 1 2 (37 / s 2 ) (7 . 1 s 1 . 3 s) 2 = 360 . 76 . 002 (part 1 of 3) 10.0 points A beetle takes a joy ride on a pendulum. The string supporting the mass of the pendulum is 160 cm long. If the beetle rides through a swing of 37 , how far has he traveled along the path of the pendulum? Correct answer: 103 . 324 cm. Explanation: Let : r = 160 cm , and θ = 37 . Arc length is defined as s = r θ = (160 cm)(37 ) · parenleftBig π 180 parenrightBig = 103 . 324 cm . 003 (part 2 of 3) 10.0 points What is the displacement experienced by the beetle while moving theough the same angle 37 ? Correct answer: 101 . 538 cm. Explanation: Using the law of cosines, we have bardbl vector R bardbl = radicalbig r 2 + r 2 2 r r cos θ = r radicalbig 2 (1 cos θ ) = (160 cm) radicalbig 2(1 cos 37 ) = 101 . 538 cm . Alternative Solution: Divide the isosce- les triangle in half. Then bardbl vector R bardbl = 2 . 0 r sin parenleftbigg θ 2 parenrightbigg = 2 . 0 (160 cm) sin 18 . 5 = 101 . 538 cm . 004 (part 3 of 3) 10.0 points If the pendulum at some instant is swinging at 2 . 5 rad / s, how fast is the beetle traveling? Correct answer: 400 cm / s. Explanation:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document