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The whole arrangement is being pulled from the right

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duces negligible friction. The whole arrangement is being pulled from the right, as indicated by the arrow in the figure, and the speed of the arrangement increases at rate a . The ten- sion on the string connecting the leftmost block to the middle block is (a) ma 4 (b) 2 ma (c) 3 ma (d) m g a (e) 3 m g a Each of the blocks accelerates at a . Looking at the leftmost block, the force of tension, ~ F , is the only force acting on it. Therefore, by ~ F m~a , the answer is choice A . 6. A small 0.42 kg metal block is connected by a 1.5 m long thin string to a peg on the center of a frictionless table. The string is pulled so that it is fully extended and then the metal block is given a sudden push which starts it moving in a circle around the peg. If the metal block performs 1.7 revolutions per second, the tension of the string is (a) 72 N 4 (b) 4.1 N (c) 1.8 N (d) 17 N (e) 36 N 6
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The motion of the block is centripetal: F c T mv 2 R Given the (constant) frequency, f , we can find the distance traveled per unit time by multiplying by the circumference: v 2 πR f Substituting in we see: T 4 π 2 mRf 2 4 π 2 . 42kg 1 . 5m 1 . 7 2 s 2 72N 7. On the surface of Earth the gravitational acceleration is g 9 . 8 m/s 2 . At an alti- tude (above the Earth’s surface) equal to half the radius of the Earth, the gravitational acceleration is Newton’s law of gravity is given as: F g GMm R 2 This implies the acceleration at the surface of Earth is: g GM R 2 9 . 81m/s 2 At an altitude half the radius of Earth: R R R 2 3 2 R Substituting this R into our acceleration expression: g GM 3 2 R 2 4 GM 9 R 2 4 9 g 4 . 4m/s 2 Good luck! 7
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