A bullet of mass 50 g moving with an initial velocity of 100 m s^-1, strikes a wooden block and comes to rest after penetrating a distance 2 cm in it. Calculate (i) initial momentum of the bullet (ii) final momentum of the bullet, (iii) retardation caused by the wooden block, and (iv) resistive force exerted by the wooden block

Given,

m = 50 g

Converting g to Kg

1000 g = 1 Kg

50 g = ($\dfrac{1}{1000}$) x 50 kg

50 g = 0.05 Kg

Hence, m = 0.05 Kg

u = 100 m s^-1

S = 2 cm

Converting cm to m

100 cm = 1 m

2 cm = ($\dfrac{1}{100}$) x 2 = 0.02 m

(i) Initial momentum of the bullet = mass (m) x initial velocity (u)

Substituting the values in the formula above we get,

Initial momentum = 0.05 x 100 = 5 kg m s^-1

Hence, Initial momentum = 5 kg m s^-1

(ii) Final momentum = mass (m) x final velocity (u)

Substituting the values in the formula above we get,

Final momentum = 0.05 x 0 = 0 kg m s^-1

Hence, Final momentum = Zero

(iii) As we know,

v² - u² = 2as

Substituting the values in the formula above we get,

$0^2 - 100^2 = 2 \times a \times 0.02 \\[0.5em] - 10000 = 0.04 \times a \\[0.5em] \Rightarrow a = - \dfrac {10000}{0.04} \\[0.5em] \Rightarrow a = - \dfrac {1000000}{4} \\[0.5em] \Rightarrow a = - 250000 \text{m s}^{-2}\\[0.5em]$

Hence,

Retardation caused by wooden block = 2.5 x 10⁵ m s^-2

(iv) Now,

Force (f) = mass (m) x acceleration (a)

Substituting the values in the formula above we get,

$F = 0.05 \times (2.5 \times 10^5) \\[0.5em] \Rightarrow F = 0.125 \times 10^5 \text{N} \\[0.5em]$

Hence,

Resistive force exerted by wooden block = 12500 N