Question

How much work is needed to be done on a ball of mass 10 kg to give it a momentum of 250 kg m/s ?

Answer 1

Answer:

w=p^2/2m

p=250

m=10

w=250*250/2*10

w=3125 jule

Answer 2

Answer: If the body starts with u = 0, the work to be done to have the momentum = 250 kg m/s is 3.125 kJ.

Explanation:

We know, KE of any body with velocity 'v' and mass 'm' is = mv²/2 __(A)

And momentum of same body = p = mv

Now, multiplying and dividing physical quantity 'm' with A:

mv²/2 = (mv²)m/2m = (mv)²/2m = p²/2m

Or, KE = p²/2m

Now, as per work energy thm,

W = ∆KE

=> W = ½ m(v² - u²) = ½ mv² (if it starts from rest) = p²/2m

=> W = KE = p²/2m

=> W = (250 kg m/s)(250 kg m/s)/(2 × 10 kg) = 3125 J