Question #54720

1 Answer
Dec 20, 2014

Solution : The speed of each bullet is #600# m/s. Understanding the solution requires knowing the definition of power .

Explanation : We are given the power of the machine gun and the firing rate (in bullets per minute). From this calculate the kinetic energy of each bullet.

#P # - Power of the machine gun.
#E_o# - Kinetic energy of each bullet.

#(dN)/(dt)# - Number of bullets fired per unit time.

#P= 7.2# kW #= 7.2\times10^{3}# W;
#(dN)/(dt) = 240# bullets/min #= 4# bullets/sec.

#P=(dE)/(dt)=d/dt (NE_o) = E_o(dN)/(dt); \qquad => E_o=P/((dN)/(dt))#
#E_o=(7.2\times10^3 J/s)/(4 \quad "bullets"/sec) = 1.8 \times 10^3 J/"bullet"#

Once the kinetic energy of each bullet is know we can calculate their velocity if their mass is given.

#E_o=1/2 mv^2; \qquad => v=\sqrt{(2E_o)/m}#
#v = \sqrt{(2\times 1.8\times 10^{3} J)/(10^{-2} kg)} = 600# m/s

Some Useful Definitions
Power : Power is the rate at which energy is transferred (transmitted/received). It is the energy transferred per unit time.
#P=(dE)/(dt), #
Since the SI unit for measuring energy is Joules , the SI unit for power is Joules/second which is defined as Watts .

Another quantity related to energy transfer rate is called Intensity. This problem does not require knowing this but it does not hurt if we know that.

Intensity : Intensity is a measure of how concentrated the power is. Intensity is defined as the Power transferred per unit area.

#I=P/A=1/A.(dE)/(dt)#

Since the SI unit for measuring power is Watt , the SI unit for intensity is Watts/second.