Question

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.

Answer 1

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

Step-by-step 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

• According to the Work-Energy principle, the work W done on an object is equal to the change in its kinetic energy ΔK.E

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