An asteroid is moving along a straight line. a force acts along the displacement of the asteroid and slows it down. the asteroid has a mass of 5.2× 104 kg, and the force causes its speed to change from 7000 to 5100m/s. (a) what is the work done by the force? (b) if the asteroid slows down over a distance of 1.4× 106 m determine the magnitude of the force.

-104 x 10^9 j and -74, 285.7 N

Explanation:

from the question we were given the following parameters

mass = 5.2 x 10^4 kg

initial velocity ( V1 ) = 7000 m/s

final velocity ( V2 ) = 5000 m/s

distance (D) = 1.4 x 10^6 m

therefore work done =  1/2 (m(V1 - V2)^2)

V1 - V2 = 5000 - 7000 = -2000 m/s

work done = 1/2 x 5.2 x 10^4 x (-2000^2)

       = -104 x 10^9 j

The work done by a force F in displacing an object by distance d is given by

W=Fd

therefore force = work / distance

force = (-104 x 10^9) / 1.4 x 10^6

        = -74, 285.7 N

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