Question

A bullet of mass 10 g travelling with a speed of 100 ms-1

impinges a wooden plank and penetrates 10 cm in it

before coming to rest, calculate resistance offered by plank.​

Answer 1

Given :

Mass of bullet = 10g = 0.01kg

Initial velocity = 100m/s

Final velocity = zero

Distance travelled = 10cm = 0.1m

To Find :

Resistive force offered by plank.

Solution :

■ First of all, we need to find acceleration of the bullet. Since, bullet has constant acceleration throughout the motion, we can apply equation of kinematics to solve this problem.

Let's apply third equation of kinematics :

→ v² - u² = 2as

• v : final velocity
• u : initial velocity
• a : acceleration
• s : distance

→ 0² - 100² = 2(a)(0.1)

→ a = 10000/0.2

→ a = -50,000 m/s²

[Note : Negative sign shows retardation]

■ As per newton's second law of motion, force is measured as the product of mass and acceleration$.$

→ F = m × a

→ F = 0.01 × (-50,000)

→ F = -500N

Answer 2

Answer:

$\huge {\green {\bf {given}}}$

• Mass of Bullet = 10 gram = 0.001kg
• Speed of bullet = 100 m/s
• Final velocity= 0
• Distance travelled = 0.1 m

$\huge {\green {\bf {To \: Find}}}$

Resistance offered by plank

According to third equation of kinematics

${v}^{2} - {u}^{2} = 2as$

${0}^{2} - {100}^{2} = 2 (a)(01)$

$\frac{10000}{0.2}$

$\frac{5000}{ {m}^{2} }$

Acceleration of bullet = 5000 m/s

According to second law of newton force is measured as the product of mass and acceleration

${f \: = m \: \times a}$

$f \: = 0.01 \times - 5000$

$\:f \: = 500 \: newton$

✴️ Extra information ✴️

$\bf {V = final \: velocity}$

$\bf {U = \: Initial \: velocity}$

$\bf {A = \: Acceleration}$

$\bf {S = \: Distance}$