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solved_problems_for_chapter_12

# solved_problems_for_chapter_12 - 12 Picture the Problem The...

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12. Picture the Problem : The 2.0-kg mass is gravitationally attracted to the other three masses. Strategy: Add the gravitational forces using the component method of vector addition. Use equation 12-1 and the geometry of the problem to determine the magnitudes of the forces. Let 1 1.0 kg, m = 2 2.0 kg, m = 3 3.0 kg, m = and 4 4.0 kg. m = Solution: 1. (a) Find the x com- ponent of the force on 2 m : ( 29 ( 29 ( 29 ( 29 ( ( 29 ( 1 2 2 4 2 2 12 24 1 2 2 4 12 1 4 12 2 2 2 2 3 24 12 24 12 24 11 2 2 2 2 8 cos 4.0 kg 0 1.0 kg 6.67 10 N m /kg 2.0 kg 0.20 m 0.20 m 0 1.3 10 N x x m m m m F G G r r m m m m r m m r G G Gm r r r r r F θ - - = + = + = + ÷ ÷ = × × + + = × 2. Find the y component of the force on 2 m : ( 29 ( 29 ( 29 ( 29 ( ( 29 ( 2 3 2 4 2 2 23 24 2 3 3 2 4 14 4 14 2 2 2 2 3 24 23 24 23 24 11 2 2 2 2 8 sin 4.0 kg 0 3.0 kg 6.67 10 N m /kg 2.0 kg 0.10 m 0.20 m 0 4.5 10 N y y m m m m F G G r r m m m m m r m r G G Gm r r r r r F θ - - = + = + = + ÷ ÷ = × × + + = × 3. Use the components of F r to find its magnitude and direction. ( 29 ( 29 2 2 2 2 8 8 8 8 1 1 8 1.3 10 N 4.5 10 N 4.7 10 N 4.5 10 N tan tan 74 below horizontal and to 1.3 10 N x y y x F F F F F θ - - - - - - - = + = × + × = × × = = = ° ÷ ÷ × 4. (b) If the sides of the rectangle are all doubled, all forces are reduced by a factor of 2 2 4; = the directions of the forces are unchanged. Insight: Doubling all the masses will quadruple the gravitational force, because the gravitational force depends upon the product of the masses of each object. Therefore, the force would stay exactly the same if we doubled all the masses and doubled the length of the sides of the rectangle. 21. Picture the Problem : The volcano on Io spews material at high speed straight upward. The mass slows down, rising to a height of 5.00 km before coming to rest momentarily under the influence of Io’s gravitation. Strategy: Use conservation of energy to relate the initial kinetic energy of the ejected material to its potential energy at the maximum altitude. This relation will allow the calculation of the surface gravity of Io.

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solved_problems_for_chapter_12 - 12 Picture the Problem The...

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