Question

A bullet of 10g strike the sand bag at a speed of 1000m/s and gets embedded after travelling 5cm.calculate. (a)Resistive force exerted by sand on bullet. (b)Time taken by bullet to come to rest

Answer 1

Initial speed of the bullet (u) = 1000 m/s

Final speed of the bullet (v) = 0 m/s

Mass of the bullet = 10 gm = 0.01 kg

Distance covered (s) = 5 cm = 0.05 m

Let the acceleration be a.

$v^2 =u^2 +2as$

$0^2 = 1000^2 + 2 \times a \times 0.05$

$a = - \frac{1000^2}{0.1}$

a = - 10000000 m/s^2

Force = mass × acceleration

Force = - 0.01 × 10000000

Force = - 100000 N

b) Let the time taken be t

$v = u +at$

$t = \frac{1000}{10000000}$

t = 0.0001 s

Answer 2

Answer:

(i) the resistive force exerted by the sand on the bullet is - 1 x 10⁵ N

(ii) the time taken by the bullet to come to rest is 1 x 10⁻⁴ s

Given :

• mass of bullet, m = 10 g = 0.01 kg
• speed of the bullet, v = 1000 m/s = 10³ m/s
• distance traveled by the bullet, d = 5 cm = 0.05 m

Explanation:

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

the acceleration of the bullet is given by;

→ v² = u² + 2as

→ 0 = (10³)² + a(2 x 0.05)

→ -0.1a = (10⁶)

→ -a = (10⁶) / 0.1

→ a = -1 x 10⁷ m/s²

The resistive force is given by;

➳ F = ma

➳F = (0.01)(-1 x 10⁷)

➳ F = - 1 x 10⁵ N

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

➝ v = u + at

➝ 0 = 10³ + (-1 x 10⁷ t)

➝ 1 x 10⁷ t = 10³

➝ t = 10³  / 10⁷

➝ t = 1 x 10⁻⁴ s