Assignment 11 Begin Date: 3/30/2018 1:30:00 PM -- Due Date: 4/6/2018 12:30:00 PM
ID: 2036315 • Letter: A
Question
Assignment 11 Begin Date: 3/30/2018 1:30:00 PM -- Due Date: 4/6/2018 12:30:00 PM End Date: 4/6/2018 12:30:00 PM (10%) Problem 4: Planet 1 has mass 3M and radius R, while Planet 2 has mass 4M and radius 2R. They are separated by center-to-center distance 8R. A rock is placed halfway between their centers at point O. It is released from rest. Ignore any motion of the planets 8R 2R 4M 3M Otheexpertta.com 33% Part (a) Derive an expression, in terms of relevant system parameters, for the magnitude of the acceleration a of the rock at the moment it is released 33% Part (b) Towards which planet is the direction of the acceleration in part a)? Grade Summary Deductions Potential Planet 1Planet 2 0% 100% Submit Hint I give up! Submissions Attempts remaining: (100% per attempt) detailed view Hints: 3% deduction per hint. Hints remaining: 2 Feedback: 4% deduction per feedback. ? 33% Part (c) The rock is released from rest at point O. Derive an expression for the speed v with which the rock crashes into a planet All content © 2018 Expert TA, LLCExplanation / Answer
Given
planet 1 mass m1 = 3M , planet2 is m2 = 4M
radius r1 = R , r2 = 2R
they were seprated by a distance from center to center is 8R
that is surface to surface the separation is (5R)
the object is placed exatly half way between the two planets
the gravitational force between two bodies of masses m1,m2 separated by a distance r is
F = G*m1*m2/r^2
so the mass m at O will be accelerated towards the planet 2 that is towards 4M planet
F1= Gm*3M/(2.5R)^2
F2 = Gm*4M/(2.5R)^2
so F2 > F1 so the object accelerates towards the planet 2
part c
work done = change in kinetic energy
and work done = -DU
the gravitational potential energy of the object = change in kinetic energy
mg(2.5*R) = 0.5*m(v2^2-v1^2)
here v1 =0 m/s
v2^2 = 2*g*2.5*R
v2 = sqrt(2*g*2.5*R )
v2 = 7sqrt(R) m/s
the object can crash the planet2 with a speed is v2 = 7 sqrt(R)