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# a8 - through 75.0 revolutions before coming to rest a Find...

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PHY 2053, Section 3794, Fall 2009, Quiz 8 1. A 3,000-kg car moving East at 15 m/s collides with a 2,000-kg car moving North. fter the collision, the cars stick together and move as a unit, at an angle of 30 North of East. a) What is the speed of the cars after the collision? East-momentum: m 1 × v 1 = ( m 1 + m 2 ) × v f cos( θ ). Thus: v f = m 1 × v 1 ( m 1 + m 2 ) × v f cos( θ ) = 3000 × 15 (3000 + 2000) × 0 . 8660 = 10 . 4 m / s . b) What is the speed of the 2000-kg car before the collision? North-momentum: m 2 × v 2 = ( m 1 + m 2 ) × v f sin( θ ). Thus: v 2 = ( m 1 + m 2 ) × v f sin( θ ) m 2 = (3000 + 2000) × 10 . 4 × 0 . 5 2000 = 13 . 0 m / s . Check: Should have m 2 × v 2 = m 1 × v 1 tan(30 ) by trigonometry, using mementa as vectors. 2. A centrifuge in a medical laboratory rotates at 5400 rev/min. When switched off, it rotates
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Unformatted text preview: through 75.0 revolutions before coming to rest. a) Find the constant angular acceleration of the centrifuge. Use ω 2 = ω 2 + 2 α × ∆ θ with ω = 0. So: α = − ω 2 2∆ θ = − ( 2 π × 5400 60 ) 2 × 1 2 × 2 π × 75 . = − 108 π = − 339 . 3 rad / s 2 . b) How long does it take to come to rest? Use: ∆ θ = ω + ω 2 × ∆ t = ⇒ ∆ t = 2∆ θ ω + ω = 2 × 2 π × 75 . × ( 60 2 π × 5400 ) = 1 . 67 sec ....
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