Mastery Problem Rubric vl PHY 2400 Spring 2016 Category Descriptions: 1. Set up

Question

Mastery Problem Rubric vl PHY 2400 Spring 2016 Category Descriptions: 1. Set up the Problem The goal here is to be clear on your starting place and your end goal, before you write a bunch of math down. a. Re-state the problem in your own words. This should only take a sentence or two, and should NOT copy all the numbers given in the original problem statement b. Identify the physical quantity that is the goal of the problem. (For example, v, the final velocity of a projectile just before it hits the ground.) c. Draw a diagram(s). You'l always need at least a simple picture of the situation. As other types of diagrams get introduced, like force diagrams, you'll add those in addition to the basic picture diagram c. Label the diagram with appropriate variables. For example, you might have a given length I, a velocity vector v showing direction for a moving object, etc. 2. Knowns and Unknowns The goal here is to take an inventory of what you know, and what you'll still need to find to complete the problem. a. List all the simple physical quantities relevant to this problem (knowns) and give values. b. List the computable physical quantities you will need to solve the problem (unknowns) 3. Plan Solution 3a. Concepts Here, you want to combine your physics knowledge with what you know about the problem (set out in steps 1 and 2, above) and plan how to get from start to finish. a. Identify the physical principles, concepts, and equations that are need to solve the problem. (For example, "Energy is conserved in this system, so Ei = Ef ") b. Arrange your basic equations in order and explain with words how each is to be used. (For example, "Ei = Ef means that mgh,--mv, so we can solve for vf...") c. If you find any missing knowns or unknowns along the way, add them to your list from step 2. 3b. Mathematics Here, you take your plan and do out the math, rearranging and substituting in equations, etc. Together with your conceptual plan, it should be easy to follow the logic of your calculations from start to finish. 4. Execute and evaluate If you haven't already plugged in numbers, do it here a. Clearly indicate your final answer, including units. b. Check that your answer is plausible-for example, if you're solving for time and got a negative number, something probably went wrong. c. If there are any extra questions posed by the problem (for example, "Is your car over the speed limit?"), answer them here

Explanation / Answer

goal:

to calculate the acceleration of one of the asteroid due to othe three.

known:

1.mass of each asteroid.

2. distance and configuration of their location

unknown: force on one asteroid due to other three

solution:

let the four asteroids are A,B,C,D such that the square ABCD exists in xy plane.

let the coordinates are:

A=(0,0)

B=(d,0)

C=(d,d)

D=(0,d)

where d=150 km=1.5*10^5 m

let their masses be M=4*10^20 kg

gravitational force is always attractive in nature.

let the force calculation is to be done on A due to other three .

force due to B:

distance =d

direction of force=+ve x axis

magnitude=G*M*M/d^2=F(let)

==>F=6.674*10^(-11)*4*10^20*4*10^20/(150*10^3)^2=4.746*10^20 N

in vector notation, force=F1=F i

force due to C:

distance =sqrt(2)*d

direction of force=45 degree with +ve x axis

magnitude=G*M*M/(2*d^2)=F/2

in vector notation, force=F2=0.5*F*(cos(45) i+sin(45) j)=0.3535*F i +0.3535*F j

force due to D:

distance =d

direction of force=+ve y axis

magnitude=G*M*M/d^2=F

in vector notation, force=F3=F j

total force=F1+F2+F3=1.3535*F i+1.3535*F j

hence force magnitude=sqrt(1.3535^2+1.3535^2)=1.9142*F=9.0847*10^20 N

direction with +ve x axis=arctan(1.3535*F/(1.3535*F))=45 degrees

then acceleration magnitude=force/mass=9.0847*10^20/(4*10^20)=2.2711 m/s^2

direction of accleeration with +ve x axis=arctan(1.3535*F/(1.3535*F))=45 degrees

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