Question

A bullet of mass 80gm is fired from a gun of mass 8kg with a velocity of 800 m/s, calculate the recoil velocity of gun

Answer 1

Mass of the bullet (m) = 80 g = 0.08 kg

Mass of the gun (M) = 8 kg

Velocity of the bullet (v) = 800 m/s

Recoil velocity of the gun (V) = ? m/s

Apply conservation of momentum ,

➠ $\sf P_{initial}=P_{final}$

➠ ( M + m ) u = mv + MV

[ ∵ Both Gun and Bullet are in rest before firing , hence initial velocity (u) of the system is zero (0) . ]

➠ ( 800 + 0.08 ) 0 = (0.08)(800)+ ( 8 ) V

➠ 0 = ( 8 ) ( 8 ) + 8V

➠ 8V = - 64

➠ V = - 8 m/s  $\pink{\bigstar}$

Note : - ve sign of recoil velocity denotes the gun moves in opposite direction to the bullet velocity .

Magnitude of recoil velocity of the gun is 8 m/s .

Answer 2

${\large{\bold{\rm{\underline{Given \: that}}}}}$

✠ Mass m of the bullet = 80 g = 0.08 kg

✠ Mass m1 of the gun = 8 kg

✠ Bullet's velocity v = 800 m/s

${\large{\bold{\rm{\underline{To \: find}}}}}$

✠ Recoil velocity v1 of gun.

${\large{\bold{\rm{\underline{Solution}}}}}$

✠ Recoil velocity of gun = 8m/s

${\large{\bold{\rm{\underline{Using \: formula}}}}}$

According to the question as we can see that there are two velocities and two masses are given so, according to the conservation of momentum,

✰ ${\sf{P_{initial} \: = P_{final}}}$

According to the question,

✰ (m1 + m)u = mv + m1v1

$\; \; \; \; \; \; \; \; \; \;{\sf{Where,}}$

★ m1 denotes mass of gun.

★ m denotes mass of bullet

★ u denotes initial velocity

★ v denotes velocity of bullet

★ v1 denotes recoil velocity of gun

⇢ (800 + 0.08)0 = (0.08)(800) + (8)v1

• Cancelling the digits
• (+ = -)
• (- = +)
• (÷ = ×)
• (× = ÷)

⇢ 0 = (8)(8) + 8v1

⇢ 0 = 8 × 8 + 8v1

⇢ 0 = 64 + 8v1

⇢ 0 - 64 = 8v1

⇢ -64 = 8v1

⇢ -64/8 = v1

⇢ -8 = v1

⇢ v1 = -8

Note - We can't take recoil velocity in negative henceforth,

⇢ v1 = 8 m/s

More knowledge -

☀ Newton's law of motion - Newton if the father of physics and he established the laws of motion in his book named ❛Principia❜ in the year 1667.

☀ Newton's first law of motion - Every body maintain it's maintain it's initial state of rest or motion with uniform speed on straight line unless an external force act on it.

◆ It's also known to be law of Galileo or law of inertia.

♛ Law of inertia = It is the property of a body by virtue of which the body opposes change in it's initial state of rest or motion with uniform speed on a straight line. There are 2 types of inertia –

⑴ Inertia of rest

⑵ Inertia of motion

Some examples of inertia –

⑴ When a coat /blanket is beaten by a stick the dust particles are removed.

⑵ When a car start suddenly the passenger bends backwards.

◆ Important - First law gives the definition of force.

♛ Force - It is that external cause which when acts on a body changes or tries to change the initial state of the body.

♛ Momentum - It is that property of a moving body and is defined of mass and velocity of the body. It's a vector quantity. SI unit is kgm/s.

$\: \: \: \: \: \: \:{\bf{Momentum = \: Mass \times Velocity}} \green\star$

☀ Newton's 2nd law of motion - The rate of change in momentum of a body is directly proportional to the applied force on the body and take place in the direction of force.

If f = force applied ; a = acceleration produced and m = mass of body the nF = ma.

◆ Newton's second law gives the magnitude of force.

◆ Newton's first law is contained in the second law.

☀ Newton's 3rd law of motion - To every action there is an equal and opposite reaction.

Some examples -

⑴ Motion of the rocket.

⑵ Recoil of the gun.