A bullet of mass 50 g is moving with a velocity of 500 m/s. If it penetrates into a 10 cm still target and comes to rest. Calculate (a) the kinetic energy possessed by the bullet (b) the average retarding force offered by the target.

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Solution

Here, m = 50 g = 50 $\times$ $10^{- 3}$ kg
u = 500 m/s
S = 10 cm
(a) K.E. = $\frac{1}{2}$ m $v^{2}$ = $\frac{1}{2}$ $\times$ 50 $\times$ $10^{- 3}$ $\times$ $500^{2}$ = 6250 J
(b) Using, $v^{2}$ - $u^{2}$ = 2aS, we get
a = $\frac{v^{2} - u^{2}}{2 a S}$ = $\frac{0^{2} - {(500)}^{2}}{2 \times 10 \times 10^{- 2}}$ = -1250000 m/ $s^{2}$
Therefore, retarding force, F = ma = 50 $\times$ $10^{- 3}$ $\times$ 1250000 = 62500 N

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A bullet of mass 50 g is moving with a velocity of 500 m/s. If it penetrates into a 10 cm still target and comes to rest. Calculate (a) the kinetic energy possessed by the bullet (b) the average retarding force offered by the target.

Here, m = 50 g = 50 × 10−3 kg u = 500 m/s S = 10 cm (a) K.E. = 12 mv2 = 12 × 50 × 10−3 × 5002 = 6250 J (b) Using, v2 - u2 = 2aS, we get a = v2−u22aS = 02−(500)22×10×10−2 = -1250000 m/s2 Therefore, retarding force, F = ma = 50 × 10−3 × 1250000 = 62500 N