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HW 6-3-solutions

# HW 6-3-solutions - madrid(tmm2353 HW 6-3 Antoniewicz(56445...

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madrid (tmm2353) – HW 6-3 – Antoniewicz – (56445) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001(part1of2)4.0points A mass of 0 . 15 kg hangs from a vertical spring in the lab room. You grab hold of the mass and throw it vertically downward. The speed of the mass just after leaving your hand is 3 . 41 m / s . While the mass moved downward a distance of 0 . 07 m, how much work was done on the mass by the Earth? Use g = 9 . 8 m / s 2 . Correct answer: 0 . 1029 J. Explanation: We can write W Earth = vector F · Δ vectorr = ( 0 , m g, 0 ) · ( 0 , Δ y, 0 ) = (0 . 15 kg)(9 . 8 m / s 2 )(3 . 41 m / s) = 0 . 1029 J . 002(part2of2)4.0points The speed of the mass has decreased to 2 . 89 m / s. How much work was done on the mass by the spring? Correct answer: 0 . 3486 J. Explanation: We can write Δ KE = W spring + W Earth W spring = Δ KE W Earth = 1 2 m vextendsingle vextendsingle vectorv f vextendsingle vextendsingle 2 1 2 m | vectorv i | 2 W Earth = 0 . 3486 J . 003(part1of6)2.0points A lithium nucleus has mass 5 . 1 × 10 - 27 kg. If its speed is 0 . 992 c (that is, v/c = 0 . 992), what is the particle energy? Use c = 3 × 10 8 m / s. Correct answer: 3 . 63599 × 10 - 9 J. Explanation: The particle energy is just the total energy, given by E = γ m c 2 . So we have E = 1 radicalBigg 1 parenleftbigg v c parenrightbigg 2 m c 2 = 1 radicalbig 1 0 . 992 2 (5 . 1 × 10 - 27 kg) c 2 = 3 . 63599 × 10 - 9 J . 004(part2of6)2.0points What is the rest energy? Correct answer: 4 . 59 × 10 - 10 J. Explanation: The rest energy is just E rest = m c 2 = (5 . 1 × 10 - 27 kg) c 2 = 4 . 59 × 10 - 10 J . 005(part3of6)2.0points What is the kinetic energy? Correct answer: 3 . 17699 × 10 - 9 J. Explanation: The kinetic energy is given by KE = E E rest = 3 . 63599 × 10 - 9 J 4 . 59 × 10 - 10 J = 3 . 17699 × 10 - 9 J . 006(part4of6)2.0points Next, an electric force acts on the lithium nucleus and does 4 . 3 × 10 - 9 J on the particle.

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