A bullet is accelerated down the barrel of a gun by hot gases produced in the combustion of gunpowder. What is the average force exerted on a 0.0100 kg bullet to accelerate it to a speed of 450 m/s in a time of 1.80 milliseconds?

A bullet is accelerated down the barrel of a gun by hot gases produced in the combustion of gunpowder. What is the average force exerted on a 0.0100 kg bullet t class=

Answer :

The average force exerted on the bullet can be calculated by using Second Newton Law:

[tex]F_{\text{avg}}=ma[/tex]

where m is the mass of the bullet and a its acceleration. Consider that acceleration is determined by the following expression (from kinematics):

[tex]a=\frac{v-v_o}{t}[/tex]

where v is the final speed of the bullet, vo the initial speed and t the time of the change of the velocity.

Then, by replacing the previous expression for a into the formula for Favg, you have:

[tex]F_{\text{avg}}=m(\frac{v-v_o}{t})[/tex]

In this case,

m = 0.0100 kg

v = 450m/s

vo = 0m/s (the bullet starts from rest)

t = 1.80ms = 1.80*10^-3 s

Replace the previous values of the parameters into the formula for Favg and simplify:

[tex]\begin{gathered} F_{\text{avg}}=(0.0100kg)(\frac{450\frac{m}{s}-0\frac{m}{s}}{1.80\cdot10^{-3}s}) \\ F_{\text{avg}}=2500N \end{gathered}[/tex]

Hence, the average force exerted on the given bullet is 2500N

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