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choli [55]
3 years ago
14

A rifle with a weight of 25 N fires a 4.5-g bullet with a speed of 240 m/s. (a) Find the recoil speed of the rifle. m/s (b) If a

650-N man holds the rifle firmly against his shoulder, find the recoil speed of the man and rifle.
Physics
1 answer:
asambeis [7]3 years ago
3 0

Answer:

The recoil speed of the man and rifle is v_{man}=0.016 ms^{-1}.

Explanation:

The expression for the force in terms of mg is as follows;

F=mg

Here, m is the mass and acceleration due to gravity.

Rearrange the expression for mass.

m=\frac{F}{g}

Calculate the combined mass of the man and rifle.

m_{man,rifle}=\frac{650+25}{g}

Put g=9.8 ms^{-2}.

m_{man,rifle}=\frac{650+25}{9.8}

m_{man,rifle}=68.88 kg

The expression for the conservation of momentum is as follows as;

m_{man}u_{man}+m_{bullet}u_{bullet}=m_{man}v_{man}+m_{rifle}v_{man,rifle}

Here, m_{man,rifle} is the mass of the man and rifle,  m_{rifle} is the mass of the rifle,u_{man},u{bullet}  are the initial velocities of the man and bullet and v_{man},v{man,rifle} are the final velocities of the man and rifle and rifle.

It is given in the problem that a rifle with a weight of 25 N fires a 4.5-g bullet with a speed of 240 m/s.

Convert mass of rifle from gram to kilogram.

m_{bullet}=4.5 g

m_{bullet}=.0045 kg

Put m_{bullet}=.0045 kg,m_{man,rifle}=68.88 kg , u_{man,rifle}=0, v_{bullet}= 240 ms^{-1} and u_{bullet}=0.

m_{man}(0)+m_{bullet}(0)=(68.88)v_{man,rifle}+(.0045)(240)

0=(68.88)v_{man,rifle}+(.0045)(240)

0=(68.88)v_{man,rifle}+1.08

(68.88)v_{man,rifle}=\frac{-1.08}{68.88}

v_{man,rifle}=-0.016 ms^{-1}  

Therefore, the recoil speed of the man and rifle is v_{man}=0.016 ms^{-1}.

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