7. A hammer of mass 400 g, moving at v ms-1, strikes a nail. The nail stops the hammer in a very short time of 0.015 s. If the force generated is – 1680N, find v.
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Initial velocity of the hammer, u = v m/s
Final velocity of the hammer, v = 0 m/s
Time taken by the hammer to stop = 0.015 s
Acceleration of the hammer = ( v - u ) / t
= ( 0 - v ) / 0.015
= - v / 0.015 m/s^2
Mass of the hammer = 400 g = 0.4 kg
Force generated = - 1680 N
We know that f = ma
Putting the values of f, m and a in the above equation :-
- 1680 = 0.4 × - v / 0.015
- 1680 = - 0.4v / 0.015
- 1680 × 0.015 = - 0.4v
- 25.2 = - 0.4v
v = - 25.2 / - 0.4r
v = 63 m/s
Ans. The value of v is 63 m/s i.e., the hammer was moving with a speed of 63 m/s.
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