Question

A rifle is firmly attached to a heavy bench, with its 75.0 cm long barrel pointing horizontally. It fires a 9.00 g bullet which leaves the muzzle at a speed of 970 m/s. assuming the acceleration of the bullet down the length of the barrel to be constant, what horizontal force does the gun exert on the bench as it fires?

Answer 1

Answer on Question 48071, Physics, Mechanics | Kinematics | Dynamics |

Question:

A rifle is firmly attached to a heavy bench, with its 75.0 cm long barrel pointing horizontally. It fires a 9.00 g bullet which leaves the muzzle at a speed of 970 m/s. assuming the acceleration of the bullet down the length of the barrel to be constant, what horizontal force does the gun exert on the bench as it fires?

Solution:

From the second Newton's law of motion we have:

$$F = m \cdot a.$$

For the case of uniform acceleration motion we can write the next equations:

$$s = \frac {a \cdot t ^ {2}}{2},$$ $$v = a \cdot t.$$

By expressing $t$ in terms of $v$ and $a$ and substituting it in equation for $s$ we obtain the acceleration $a$:

$$a = \frac {v ^ {2}}{2 \cdot s}$$

Therefore:

$$F = m \cdot a = m \cdot \frac {v ^ {2}}{2 \cdot s} = \frac {0.009kg \cdot \left(970 \frac {m}{s}\right) ^ {2}}{2 \cdot 0.75m} = 5645.4\ N$$

Answer:

$$F = 5645.4\ N$$

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