Question

If a bullet of mass 5 gm moving with velocity 100 m /sec, penetrates the wooden block upto
6 cm. Then the average force imposed by the block on the bullet is
a) 417 dine
b) 417 N
c) - 417 N
d) Zero
the key is given as option c , I need the solution

Answer 1

Given:

• Mass of bullet, m = 5 gm 5/1000 kg = 0.005 kg
• Initial velocity of bullet, u = 0
• Distance for which bullet penetrated the wooden block, s = 6 cm = 6/100  m = 0.06 m
• Final velocity of bullet, v = 0   [ since bullet will come to rest after penetrating 6 cm ]

To find:

• Average force imposed by block on the bullet, F =?

Formulae required:

• Third equation of motion

     v² - u² = 2 a s

• Newton's second law expression

    F = m a

[ Where v is final velocity, u is initial velocity, a is acceleration, s is distance covered, F is force applied and m is mass of body ]

Solution:

Let, acceleration of bullet be a

so, Using third equation of motion

→ v² - u² = 2 a s

→ ( 0 )² - ( 100 )² = 2 a ( 0.06 )

→ - 10000 = 0.12 a

→ a = -83333.34 m/s²

[Since, after penetrating a specific distance bullet came to rest therefore, force exerted by bullet on block will be equal in magnitude to the force exerted by block on bullet]

So, Using Newton's second Law expression

→ F = m a

→ F = ( 0.005 ) ( -83333.34 )

→ F = -416.67 N

→ F ≈ -417 N

Therefore,

• Force imposed by block on bullet is -417 N.

[ That means force applied has a magnitude of about 417 Newton in the direction opposite to the direction of bullet ]

Answer 2

$\huge \mathbb{\underbrace{\red{Question\:}}}$

If a bullet of mass 5 gm moving with velocity 100 m /sec, penetrates the wooden block upto 6 cm. Then the average force imposed by the block on the bullet is

a) 417 dine

b) 417 N

c) - 417 N

d) Zero

Given:-

u = 100m/s ; s = 6cm ; v = 0

To Find:-

a = ? ; F = ?

Formulas:-

• v = u + at
• v² - u² = 2as
• s = ut + 1/2 at²
• a = v - u/t
• F = ma

$\huge\blue{\boxed{\sf Solution}}$

u = 100m/s ; s = 6cm ; v = 0 ; a = ?

v² - u² = 2as

0² - 100² = 2a(0.06)

-10000 = 0.12a

a = 10000/0.12

a = 83,333.3333

Now,

Force imposed by the block on the bullet is

F = ma

F = 0.005 × 83,333.333

F = 416.66

Hence Verified