hw5b - HW#5b Page 1 of 4 Problem 1. Practice with...

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HW#5b Page 1 of 4 Problem 1. Practice with proportions. Two masses a distance R apart attract each other with a gravitational force F. For each of the cases below, give the factor by which F is changed, if: a.) if R is multiplied by 3 , then F new = · F old b.) if R is multiplied by 3.9 , then F new = · F old c.) if R is divided by 2 , then F new = · F old Solution. The equation that we are analyzing is 12 2 Gm m F R = We can see that it is proportional to 1/r 2 - that is to say, the equation divides by the square of R. So, if R is multiplied by a certain factor, the force is divided by the square of that factor. Or, equivalently, the force is multiplied by (1/(the factor))^2. (a) The factor is 3. So () 2 new old old 1 * 0.111111 3 FF F ⎛⎞ == ⎜⎟ ⎝⎠ (b) The factor is 3.9. So 2 new old old 1 * 0.0657 3.9 F (c) The factor is 0.5. So 2 new old old 1 *4 0.5 F Never forget the power of square. 10 inch Pizza = FOUR 5 inch pizza. To reduce the radius to half, you reduce the area to ¼. To increase the distance by a fact of two, you reduced the gravity force by a fact of 4. Problem 2. Mass A ( 5 kg) and mass B ( 4 kg) sit on the ground, 5 m apart. a.) What is size of the gravitational force: on A from B? N on B from A? N b.) What is the size of the gravitational force: on A from the Earth? N on B from the Earth? N c.) Explain why we normally only worry about the gravitational force on such objects from the Earth, and don't worry about including the gravitational force on objects from each other. (d.) Do A and B exert forces back on the Earth itself? If so, are those forces of smaller, equal, or larger size than your answers for part b? same size In this problem, be especially wary of round-off; keep 2-3 (non-zero) digits in each answer and throughout your calculations. Solution. (a) There is just one force to calculate, since these are Newton's-Third-Law paired forces, equal and opposite. A attracts B with the same amount of force as B attracts A ( )( ) 11 2 2 11 22 6.67 10 N-kg /m 5 kg 4 kg F= 5.336 10 5 m AB x Gm m x N r (b) Now put in Earth's mass in place of m B and Earth's radius in place of the 5-m distance.
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This note was uploaded on 08/25/2010 for the course PHYS 111 taught by Professor Jamesm.lockhart during the Spring '09 term at S.F. State.

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hw5b - HW#5b Page 1 of 4 Problem 1. Practice with...

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