Question

A bullet of 10 g strikes a sand bag at a speed of 1000 m/s and gets embedded after travelling 5 cm.
Calculate a) the resistive force exerted by the sand on the bullet.
b) the time taken by the bullet to come to rest.

Answer 1

Given,

Mass of bullet = 10 gm = 0.01 kg
initial velocity (u)of bullet = 1000 m/s
final velocity (v) = 0 m/s (because it has stopped after striking sand)
displacement of bullet = s = 5 cm = 0.05 m
a) Using 2as = v ²-u²
2(a)(0.05)=0²-1000²
2a(5/100)=-1000000
2a(1/20)=-1000000
a(1/10)=-1000000
a=−10000000=−107m/s2
acceleration of bullet is −107m/s2=−10000000m/s2
by using F=ma
F = 0.01(-10000000)
F = (1/100)(-10000000)
F = -100000 N
Therefore resistive force of bullet = -100000 N.
b) By using, v = u + at
a = (v-u)/t
-10000000 = (0-1000)/t
-10000000 = -1000/t
1/10000 = t
or
t = 10−4 seconds.