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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 3.8x 104 kg, and the force causes its speed to change from 6700 to 4600m/s. (a) What is the work done by the force? (b) If the
asteroid slows down over a distance of 2.4x 10 m determine the magnitude of the force.

Sagot :

The work done by the force is 7. 89 * 10^8 Joules and the magnitude of the force is 3. 3* 10 ^7 Newton

How to determine the work done

a. Work done = force * change in velocity = Impulse

Note that:

Force = mg

mass = 3.8x 104 kg

g = 10m/s²

Substitute into the formula for force

Force = 3.8* 10^4 * 10= 3.8* 10^5 Newton

Change in velocity = 6700 - 4600 = 2100 m/s

Work done = force *change in velocity

Work done =  3.8* 10^5 * 2100

Work done =  7. 89 * 10^8 Joules

b. Magnitude of the force = work done ÷ distance

Force = [tex]\frac{7. 89 * 10^8 }{2.4* 10}[/tex]

Force = 3. 3* 10 ^7 Newton

Therefore, the work done by the force is 7. 89 * 10^8 Joules and the magnitude of the force is 3. 3* 10 ^7 Newton

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