Question

A bullet of mass 10 gram travelling horizontally with a velocity of 150 metre per second strikes a stationary wooden block and comes to rest in 0.03 second calculate the distance of integration of the bullet into the block also calculate the magnitude of the force exerted by the wooden block on the bullet​

Answer 1

GIVEN :

• Mass of bullet = 10 gm

=> 10/1000

=> 1/100 kg

• Initial velocity (u) = 150 m/s

• Final velocity (v) = 0 m/s

• Time (t) = 0.03 sec

FIND :

We have to calculate the distance of integration of the bullet into the block and also calculate the magnitude of the force exerted by the wooden block on the bullet.

SOLUTION :

We know that..

$\star{ \bold{ \boxed{v \: - \: u \: = \: at}}}$

Put the known values in above formula

=> 0 - 150 = a(0.03)

=> - 150 = 0.03a

=> a = - 5000 m/s²

Now,

$\star{ \bold{ \boxed{v ^{2} \: - \: u ^{2} \: = \: 2as}}}$

(Thrid equation of Motion)

Put the known values in above formula

=> (0)² - (150)² = 2(-5000)s

=> - 22500 = - 10000s

=> 10000s = 22500

=> s = 2.25 m

So,

$\star{ \bold{ \boxed{F\: = \: ma}}}$

=> F = $\dfrac{1}{100}$ × (-5000)

=> F = - 50 N

______________________________

Distance of integration of bullet in the block is 2.25 m and Force exerted by wooden block is - 50 N.

____________ [ ANSWER ]

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Answer 2

$\bigstar$ Answer :

Force exerted by wooden block is - 50 N and Distance of integration of bullet in the block is 2.25 m.

$\bigstar$ Explanation :

Given that :

• Time (t) = 0.03 seconds.
• Initial velocity (u) = 150 m/s.
• Final velocity (v) = 0 m/s.
• Mass of bullet = 10 g.

Now, First of all convert Mass into Kg.

So,

⇒ $\dfrac{10}{1000}$

⇒ $\dfrac{1}{100}$ kg

We have :

• Time (t) = 0.03 seconds.
• Initial velocity (u) = 150 m/s.
• Final velocity (v) = 0 m/s.
• Mass of bullet = $\dfrac{1}{100}$ kg.

We know that :

$\bigstar\;\boxed{\sf at = v - u}}}\\ \\ \\ \star\textbf{\underline{\underline{Values in Equation,}}}}\\ \sf \\ \implies a(0.03)=0 - 150\\ \\\implies 0.03a= - 150\\ \\\implies a = -5000 m/s^2$

We also know that :

$\bigstar{\boxed{\sf v^2 - u^2= 2as}}\\ \\\star\textbf{\underline{\underline{Values in Equation,}}}}\\\sf \\\implies (0)^2 - (150)^2 = 2(-5000)s\\ \\\implies -22500 = -10000s\\ \\\implies 10000s = 22500\\ \\\bf \\\implies s = 2.25 m$

So,

$\bigstar\;\boxed{\sf ma= F}}}\\ \\\star\textbf{\underline{\underline{Values in Equation,}}}}\\\sf\\\implies \dfrac{1}{100} \times (-5000) = F\\ \\\implies F = - 50 N\\ \\ \\\bigstar\textbf{\underline{\underline{Hence, We get the answer.}}}$

∴ Force exerted by wooden block is - 50 N and Distance of integration of bullet in the block is 2.25 m.