Question

Using second law of motion , derive the relation between force and acceleration .
A bullet of 10 g strikes a sand-bag at a speed of 103 m/s and gets embedded after travelling 5 cm . calculate :
(i) the resistive force exerted by sand on the Bullet
(ii) the time taken by the bullet to come to rest .

Answer 1

Answer:

i) F = 10^5 N

ii) $t = {10}^{ - 4} s$

Explanation:

Given:

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: m = 10g = \dfrac{10}{1000} kg$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: u = {10}^{3} \frac{m}{s}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: v = 0$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: s = \dfrac{5}{100}$

To Find:

(i) the resistive force exerted by sand on the Bullet

(ii) the time taken by the bullet to come to rest .

Procedure:

i)

$\bf \boxed{ {v}^{2} - {u}^{2} = 2a.s }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: 0 - ( {10 ^{3} )}^{2} = 2.a \dfrac{5}{100 }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \:a = \dfrac{ - 1000 \times 1000}{2.5} \times 100$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: a = {10}^{7} {ms}^{ - 2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: F = m.a = 10^{5} N$

ii)

$\bf {\boxed{v = u + at}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: 0 = {10}^{3} - {10}^{7} t$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: 10 {}^{7} t = {10}^{3}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: t = \dfrac{ {10}^{3} }{ {10}^{7} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: t = {10}^{ - 4} s$

Extra points to remember for chapter Motion!!

• Displacement is the distance in a particular direction. A vector quantity.

• Speed is the rate of change of distance. S = D/T

Answer 2

Answer:

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