Chap4 - 7 Strategy Graph the vectors and their sum Use the...

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7. Strategy Graph the vectors and their sum. Use the scale of the graph to find the magnitude of the vector sum. Solution The length of the vector sum is approximately equal to seven sides of a grid square, so the magnitude is 14 N. The vector points east, so the vector sum of the forces is 14 N to the east. (Note that F r and the vector sum overlap.) D E F D + E + F N 26. Strategy Use Newton’s second law. Solution Compute the acceleration of the automobile. 3 2 3 3.36 10 N forward 2.40 m s forward 1.40 10 kg m Σ × = = = × F a r r 42. Strategy The gravitational field strength is given by 2 . g GM R = Use the mass of the Earth and the gravitational field strength of the Moon and solve for R , which, in this case, is the distance from the center of the Earth. Then, subtract the radius of the Earth to find the height above the surface. Solution Solving for R , we have 11 2 2 24 4 2 (6.674 10 N m kg )(5.974 10 kg) 1.57 10 km. 1.62 m s GM R g × × = = = × So, the height above the surface is 4 3 3 1.57 10 km 6.371 10 km 9.3 10 km . × × = × 54. (a) Strategy
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