Question

A 0.11 g bullet leaves a pistol at 323 m/s, while a similar bullet leaves a rifle at 396 m/s. It can be assumed that the forces exerted on both bullets by the expanding gasses in the guns have the same magnitude. Explain the difference in the exit speeds.

Answer 1

The difference in bullet exit speeds is due to the longer time duration or barrel length over which the same force is applied in a rifle compared to a pistol. This results in a greater impulse and, consequently, a greater change in momentum for the bullet from a rifle.

Step-by-step explanation:

The difference in the exit speeds of the bullets from the pistol and the rifle, despite the same magnitude of force being exerted, can be attributed to the concept of impulse. The impulse experienced by an object is the product of the average force applied to it and the duration of time for which this force is applied. The impulse imparts a change in momentum to the object. If the forces on the two bullets are the same, but the rifle provides this force over a longer barrel length or time duration than the pistol, the rifle bullet will experience a greater impulse, leading to a higher exit speed. This is an application of the impulse-momentum theorem, which states that the change in momentum of an object is equal to the impulse applied to it.

Answer 2

Explanation;

Mass of both the bullets = 0.11 g = 0.00011 kg

The length of pistol's barrel in meters= L

The length of rifle's barrel in meters= l

Exit speed of the bullet from pistol :

`v_(1)^2=u_(1)^2+2a_1L`

`u_(1)^2=0` (bullet was initially at rest)

`a_1=(v_(1)^2)/(2L)`

Force on the bullet by the pistol

`F_1=0.00011 kg* (v_(1)^2)/(2L)`..(1)

Exit speed of the bullet from Riffle :

`v_(2)^2=u_(2)^2+2a_2l`

`u_(2)^2=0` (bullet was initially at rest)

`a_2=(v_(2)^2)/(2l)`

`F_2=0.00011 kg* (v_(2)^2)/(2l)`..(2)

Given
`F_1=F_2`

`0.00011 kg* (v_(1)^2)/(2L)=0.00011 kg* (v_(2)^2)/(2l)`

`((v_1)/(v_2))^2=(L)/(l)`

`Speed\propto Length`

From this we can say that speed of the bullet is directly related to the length of the barrel of the firearm.

The higher speed of the bullet from riffle means that barrel length of the riffle is longer in which bullet is accelerated through longer distance.The longer length of riffles barrel explains the higher speed of the bullet when shot from the riffle.