solved_problems_for_chapter_12

solved_problems_for_chapter_12 - 12. Picture the Problem:...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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 - - = + = + = + ÷ ÷ = × × + + = × 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 - - - - - - - = + = × + × = × × = = = ° ÷ ÷ × 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.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/05/2012 for the course CHEM 3321 taught by Professor Bean during the Spring '11 term at American Jewish University.

Page1 / 5

solved_problems_for_chapter_12 - 12. Picture the Problem:...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online