"a problem involves a car of mass m going down a track from a height h, and round a loop of radius r. the loop is frictionless.
it asks for the minimum cut-off speed required, at the highest point in the loop (call it point d), such that the car makes it round the loop without falling. i know the solution; i should set the centripetal accleration equal to 9.81. in other words, contact force with the track at point d is equal to zero.
but i tried solving it by conservation of energy. at point d, the car is at a height 2r from ground level. therefore, in order for the car to reach that height at point d, it must initially have a potential energy of mg(2r). meaning, it should be released from a height h = 2r.
i got the wrong answer and i'm confused why that happened. isn't that how conservation of energy work? clarify, where's the error in my solution? "

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.

conduction, convection, radiation

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