Ch3 HW3
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Ch3 HW3

Course Number: PHYS 2212, Spring 2010

College/University: Georgia Tech

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WebAssign Ch3 HW3 (Homework) Current Score: 24 out of 24 Due: Friday, September 12, 2008 09:00 AM EDT Description Iterative prediction of motion; gravitational force; electric force; reciprocity Instructions Reading: Sec. 3.7-3.12 (and review Sec. 3.4-3.6) Arthur Barfield PHYS 2211, section M, Fall 2008 Instructor: Jennifer Curtis The due date for this assignment is past. Your work can be viewed below, but no...

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Ch3 WebAssign HW3 (Homework) Current Score: 24 out of 24 Due: Friday, September 12, 2008 09:00 AM EDT Description Iterative prediction of motion; gravitational force; electric force; reciprocity Instructions Reading: Sec. 3.7-3.12 (and review Sec. 3.4-3.6) Arthur Barfield PHYS 2211, section M, Fall 2008 Instructor: Jennifer Curtis The due date for this assignment is past. Your work can be viewed below, but no changes can be made. 1. [MI2 03.P.49] 8/8 points (a) In outer space, far from other objects, block 1 of mass 60 kg is at position < 10, 8, 0 > m, and block 2 of mass 1400 kg is at position < 19, 8, 0 > m. What is the (vector) gravitational force acting on block 2 due to block 1? It helps to make a sketch of the situation. = < -6.948E-8 -6.95e-08 , 0 0 ,0 0 >N grav (b) At 4.1 seconds after noon both blocks were at rest at the positions given above. At 4.3 seconds after noon, what is the (vector) momentum of block 2? = < -1.389e-8 -1.39e-08 , 0 0 ,0 0 > kgm/s 1 (c) At 4.3 seconds after noon, what is the (vector) momentum of block 1? = < 1.389e-8 1.39e-08 , 0 0 ,0 0 > kgm/s 2 At 4.3 seconds after noon, which one of the following statements is true? Block 1 is moving faster than block 2. Block 1 and block 2 have the same speed. Block 2 is moving faster than block 1. Solution or Explanation (a) Calculate the magnitude of the gravitational force as Gm m /| 1 2 2 - 1 | . The force is in the -x 2 direction. (b) Update the momentum using the gravitational force in the momentum principle. Since the force is in the -x direction, and the block started from rest, the new momentum is in the -x direction. (c) Just multiply all components from part (c) by -1, since the magnitude of the force is the same but the direction is opposite. 2. [MI2 03.X.15.01] 4/4 points Suppose you are going to program a computer to carry out an iterative calculation of motion involving nonconstant forces. Which of the following calculations should be done before starting the repetitive "loop" calculations? Update the (vector) position of each object Specify an appropriate value for the time step Specify the mass of each object Calculate the (vector) forces acting on the objects Specify the initial (vector) momentum of each object Define constants such as G Specify the initial (vector) position of each object Update the (vector) momentum of each object Inside the repetitive "loop", assuming that we use the final velocity in each time interval as the approximation to the average velocity in that time interval, what should be the sequence of calculations? 1: Calculate the (vector) forces acting on the objects Calculate the (vector) forces acting on the objects 2: the Update (vector) momentum of each object Update the (vector) momentum of each object 3: Update the (vector) position of each object Update the (vector) position of each object 3. [MI2 03.P.50] 12/12 points (a) Two thin hollow plastic spheres, about the size of a ping-pong ball with masses (m =m = 1 2 2e-3 kg) have been rubbed with wool. Sphere 1 has a charge q = -5e-9 C and is at location < 1 30e-2, -20e-2, 0 > m. Sphere 2 has a charge q = -5e-9 C and is at location < -20e-2, 50e-2, 2 0> m. It will be useful to draw a diagram of the situation, including the relevant vectors. What is the relative position vector pointing from q to q ? 1 2 = < -.5 -0.5 , .7 0.7 , 0 What is the distance between q and q ? 1 2 0 >m | | = .8602 0.86 m What is the unit vector in the direction of ? = < -.5812 -0.581 , .8137 0.814 , 0 0> What is the magnitude of the gravitational force exerted on q by q ? 2 1 | grav on q | = 3.62e-16 2 3.62e-16 N 2 1 What is the gravitational force (vector) exerted on q by q ? grav on q = < 2.105e-16 2 2.11e-16 , -2.947e-16 ? -2.95e-16 , 0 -0 > N What is the value of 3.04e-7 3.04e-07 N 2 1 What is the electric force (vector) exerted on q by q ? electric on q = < -1.767e-7 2 -1.77e-07 , 2.47438e-7 2.47e-07 , 0 0 >N (b) What is the ratio of the magnitude of the electric force to the magnitude of the gravitational force? = 8.398e8 8.40e+08 (You see that electric forces between two small charged objects are typically very much larger than gravitational forces between those same small objects. It takes the entire mass of the Earth to exert a sizable gravitational force on a small object.) (c) If the two masses were 4 times farther away (that is, if the distance between the masses were 4* , what would be the ratio of the magnitude of the electric force to the magnitude of the gravitational force now? = 8.398e8 8.40e+08 Solution or Explanation The relative position vector is "final" minus "initial": calculate the position vector of sphere 2 minus the position vector of sphere 2. The distance between the two spheres is the magnitude of the relative position vector | |. The unit vector is found by dividing the components of by its magnitude | |. | grav | = GM M /r , and the magnitude of the gravitational force is the same for both objects. 1 2 2 The calculation of the electric force is very similar to the calculation of the gravitational force, but it involves the charges rather than the masses, and the electric constant is different from the gravitational constant. Since both kinds of force are inversely proportional to the square of the distance, the ratio of these two forces is same at all distances.

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