HW 5-3-solutions - madrid (tmm2353) HW 5-3 Antoniewicz...

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Unformatted text preview: madrid (tmm2353) HW 5-3 Antoniewicz (56445) 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 20.0 points A small block of mass m is attached to a spring with stiffness k s and relaxed length L . The other end of the spring is fastened to a fixed point on a low-friction table. The block slides on the table in a circular path of radius R > L . How long does it take for the block to go around once? 1. T = radicalBigg 4 2 mR 2 k s ( R L ) 2. T = radicalBigg 2 mR k s ( R L ) 3. T = radicalBigg 4 2 mR k s ( R L ) correct 4. T = radicalBigg 4 mR k s ( R L ) 5. T = radicalBigg 3 2 mR 2 k s ( R L ) Explanation: The net force on the ball is equal to the force by the spring on the ball, which is vextendsingle vextendsingle vextendsingle vector F spring vextendsingle vextendsingle vextendsingle = k s s. The distance the spring stretches is s = R L . Because the speed of the ball is constant and is much less than the speed of light, vextendsingle vextendsingle vextendsingle vector F net vextendsingle vextendsingle vextendsingle = m | vectorv | 2 R . So we have vextendsingle vextendsingle vextendsingle vector F spring vextendsingle vextendsingle vextendsingle = k s s and vextendsingle vextendsingle vextendsingle vector F net vextendsingle vextendsingle vextendsingle = | F spring | m | vectorv | 2 R = k s ( R L ) | vectorv | = radicalbigg k s R ( R L ) m . For circular motion, | vectorv | = 2 R/T . We substitute: 2 R T = radicalbigg k s R ( R L ) m T = radicalBigg 4 2 mR k s ( R L ) . 002 20.0 points You put a 32 kg object on a bathroom scale at the North Pole, and the scale reads exactly 32 kg. At the North Pole, you are 6357 m from the center of the Earth. At the equator, the scale reads a different value due to two effects: 1) the Earth bulges at the equator due to its rotation, and you are 6378 m from the center of the Earth, and 2) you are mov- ing in a circular path due to the rotation of the Earth. Taking into account both of these effects, what does the scale read at the equa- tor? Use G = 6 . 67 10 11 N m 2 / kg 2 and M e = 6 10 24 kg....
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HW 5-3-solutions - madrid (tmm2353) HW 5-3 Antoniewicz...

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