A bullet of 10g strikes a sand-bag at a speed of 1000m/s and gets embedded after travelling 5 cm. (i)the resistive force exerted by Sand on the bullet. (ii) the time taken by bullet to come to rest.
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(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 Parameter :
- 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
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