(The Potential Function in Two Dimensions) Two point masses, m1 and m2, lie in t
ID: 2295379 • Letter: #
Question
(The Potential Function in Two Dimensions) Two point masses, m1 and m2, lie in the xy- plane, with m1 held in place at the origin and m2 free to move at a distance r away at a point P having coordinates x and y. The gravitational potential energy of these massesis found to be:U(r)= (-Gm1m2x)/r
a.)What are the x and y components of the gravitational force? (Hint: Put r in terms of x and y) b.)What is the magnitude of the gravitational force? c.)Does m1 attract or repel m2? How do you know? (The Potential Function in Two Dimensions) Two point masses, m1 and m2, lie in the xy- plane, with m1 held in place at the origin and m2 free to move at a distance r away at a point P having coordinates x and y. The gravitational potential energy of these massesis a.)What are the x and y components of the gravitational force? (Hint: Put r in terms of x and y) b.)What is the magnitude of the gravitational force? c.)Does m1 attract or repel m2? How do you know?
Explanation / Answer
(1)U(x) = -Gm1m2/x
F = - dU/dx = -Gm1m2/x^2.
(2) Presence of minus sign indicates that force is opposite to the positive x direction. Hence the force is attractive.
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