Question

PROBLEM: A machine gun fires 360 bullets per minute an each bullet travels w
velocity of 600 m/sec of the mass of each bullet is 5gm, find the power of the mass gun​

Answer 1

Given :-

Total number of bullets = 360 bullets

Mass of each bullet = 5 g

Velocity travelled by each bullet = 600 m/s

To Find :-

The power of the gun.

Analysis :-

You can easily find the kinetic energy by substituting the given values in the question in it's respective formula.

Then substitute the values such that power is equal to energy by time and find the power of the gun accordingly.

Solution :-

We know that,

• v = Velocity
• m = Mass
• KE = Kinetic energy
• e = Energy
• p = Power
• t = Time

According to the question,

Mass of each bullet = 5 g = 0.005 kg

No. of bullet = 360

Bullets per min = 360/60 = 6 bullet

No. of bullets fired in sec = 6t

Total mass of the bullets = 0.005 × 6t = 0.03t kg

Using the formula,

$\underline{\boxed{\sf Kinetic \ energy= \dfrac{1}{2} mv^2}}$

Given that,

Mass (m) = 0.03t kg

Velocity (v) = 600 m/s

Substituting their values,

$\sf KE=\dfrac{1}{2} \times 0.03t \times (600^2)$

$\sf KE=\dfrac{1}{2} \times 0.03t \times 360000$

$\sf KE=1800 \times 3t$

$\sf KE=5400t \ J$

Using the formula,

$\underline{\boxed{\sf Power=\dfrac{Energy}{Time \ taken} }}$

Given that,

Energy (e) = 5400t J

Time (t) = t

Substituting their values,

$\sf p=\dfrac{5400t}{t}$

$\sf p=5400 \ W=5.4 \ kW$

Therefore, the power of the gun is 5.4 kW.

Answer 2

Answer:

Given :-

• Total number of bullets = 360 bullets
• Mass of each bullet = 5 g

• Velocity travelled by each bullet = 600 m/s

To Find :-

Power of the gun

Solution :-

$\sf \green {mass = \dfrac{5}{1000} = 0.005 \: kg}$

$\sf \red {bullet \: fire \: in \: 1 \:min = \dfrac{360}{60} = 6}$

$\sf \blue {bullet \: fire \: in \: 1 \: sec = 6t}$

$\sf \pink {total \: mass \: of \: bullet = 0.005 × 6t = 0.03t kg}$

$\huge \bf \blue {KE = \frac{1}{2} {mv}^{2} }$

$\bf \pink {KE = \dfrac{1}{2} \times 0.03t \times (600) {}^{2} }$

$\bf \orange {KE = \dfrac{1}{2} \times 0.3t \times 360000}$

$\bf \red {KE = 1 \times 0.3t \times 180000}$

$\bf \blue {KE = 3t \times 1800}$

$\huge \tt \: KE = 5400t$

$\huge \bf \blue {Power= \dfrac{Energy}{Time}}$

$\sf \green {Power= \dfrac{5400t}{t}}$

$\huge \bf \: Power= \: 5400 \: w$