s11 - Solutions to Homework#1 Chapter 19 2 Picture the...

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Solutions to Homework #1 Chapter 19 2. Picture the Problem: An electrically neutral object is given a negative charge. Strategy: Each electron carries both charge and mass, so adding or subtracting electrons will change the object’s mass. Solution: 1. (a) Giving the object a negative charge requires the addition of electrons, which have mass. We conclude that the object’s mass will increase as a result of being charged. 2. (b) The best explanation is I. To give the object a negative charge we must give it more electrons, and this will increase its mass. Statement II is false, and statement III fails to distinguish between charge and mass conservation. Insight: Likewise, giving an object a positive charge requires the removal of electrons, decreasing the object’s mass. 20. Picture the Problem: Two charges of unequal magnitude exert an electrostatic force on each other. Strategy: Use Coulomb’s law (equation 19-5) to find the magnitude of the force between the two charges. Solution: 1. (a) Apply equation 19-5 directly: ( 29 ( 29 ( 29 ( 29 6 6 1 2 9 2 2 2 2 3.13 10 C 4.47 10 C 8.99 10 N m / C 1.93 N 0.255m q q F k r - - = = = 2. (b) The magnitude of the electrostatic force depends upon the product of the charges of both particles, so the negative charge experiences a force magnitude that is the same as that experienced by the positive charge. Insight: The forces experienced by the two charges must also be the same magnitude and opposite in direction in order to be consistent with Newton’s Third Law. 32. Picture the Problem: Four charges are situated at the corners of a square as shown in the diagram at the right. Strategy: The force on charge q 3 is a vector sum of the forces from the other three charges. Let q 3 be at the origin and q 2 be on the negative x - axis. Use Coulomb’s law (equation 19-5) to find the vector sum of the three forces, from which we can find the magnitude and direction of the net electrostatic force on q 3 . Solution: 1. (a) Find 2 F r : ( 29 ( 29 2 3 2 2 2 2 2.0 3.0 6.0 ˆ ˆ k q q k q q kq d d d = = = F x x r 2. Find 4 F r : ( 29 ( 29 3 4 4 2 2 2 3.0 4.0 12 ˆ ˆ k q q k q q kq d d d = = = F y y r 3. Find 1 F r : ( 29 ( 29 ( 29 ( 29 ( 29 2 1 3 1 2 2 2 3.0 ˆ ˆ ˆ ˆ 3.0 2 ˆ ˆ 4 2 2 2 2 2 2 k q q k q q kq d d d = - - = - - = - - x y x y F x y r 4. Find the vector sum of the three forces: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 net 2 2 2 2 2 2 2 9 2 2 6 2 net 6.0 3.0 2 12 3.0 2 ˆ ˆ 4 4 3.0 ˆ ˆ 2.0 2 4 4 2 4 3.0 8.99 10 N m / C 2.4 10 C ˆ ˆ 2.0 2 4 4 2 4 0.27 m ˆ ˆ 3.5 N 7.8 N kq kq kq kq d d d d kq d - = - + - = - + - ״ = - + - = + F x y x y x y F x y r r
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5. Find the direction of net F r from the + x axis: net, 1 1 net, 7.8 N tan tan 66 3.5 N y x F F θ - - = = = 6. Find the magnitude of net F r : ( 29 ( 29
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s11 - Solutions to Homework#1 Chapter 19 2 Picture the...

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