How Far Does a Bullet Travel When a Gun Recoils 2mm?

In summary, the problem involves a 500g pistol at rest on a frictionless table that accidentally discharges and shoots a 10g bullet parallel to the table. Using the equation 0=m1v1+m2v2 and substituting the value of velocity as displacement over time, the bullet's displacement is calculated and found to be -0.1m. Converting this to centimeters, the final displacement of the bullet is 9.8 cm. However, it is also noted that this can be solved by considering the conservation of momentum and the fact that the center of mass of the system remains constant.
  • #1
kateman
114
0

Homework Statement


A 500g pistol lies at rest on an essentially frictionless table. It accidentally discharges and shoots a 10g bullet parallel to the table. How far has the bullet moved by the time the gun has recoiled 2.00mm?


Homework Equations


0=m1v1+m2v2
m1v1= (m1+m2)Vf


The Attempt at a Solution


well i tried the 0=m1v1+m2v2 formula and tried to substitute the value of v as s/t and then eliminating time, i rearranged it for the displacement value of the bullet and got a weird value of -.1 when the answer is 9.8cm
i know now that this is the wrong way to approach it when i consider the conservation of momentum but i have no other ideas on how to do this or how to start it!

if anyone does it would be most appreciated!
 
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  • #2
There's nothing at all wrong with your approach, or even your answer, depending upon the units you are using. Realize that if the gun goes moves one way (+ say), then the bullet will move in the opposite direction (call it -).

0.1 m = 10 cm. If you subtract the 2 mm (0.2 cm) that the gun moved you'll get 9.8 cm. (But I see no reason why you would subtract the gun's movement from the bullet's, so I disagree with that answer.)
 
  • #3
Well, the force pushing the bullet is pushing back on the gun.

So F=ma

then both bullet and gun are starting at rest, and force applied over distance (F*d) is energy, and the energy is kinetic.

Assume constant acceleration. The lighter mass accelerates faster.

http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html
 
  • #4
ahh yeah converting back to cm might help :P

hmm that's very interesting (what you found), but i agree, it does seem to be just a random coincidence

yup, its all good now, thanks to both of you
 
Last edited:
  • #5
Also realize that the (perfectly valid) approach that you took is equivalent to noting that the center of mass of "bullet + gun" does not change. If the gun moves 2mm to the left, then the bullet must move 10 cm to the right to maintain the center of mass.
 
  • #6
yeah i do now thanks
 

1. How does a bullet travel through the air after being fired from a gun?

When a bullet is fired from a gun, it is propelled forward by the force of the expanding gases from the gunpowder. The bullet also spins due to the rifling in the barrel of the gun, which helps stabilize its flight. As the bullet travels through the air, it experiences drag and gravity, which cause it to slow down and eventually fall to the ground.

2. How fast does a bullet travel after being fired from a gun?

The speed of a bullet after being fired from a gun can vary depending on the type of gun and bullet used. Generally, handgun bullets travel at speeds of around 800-1200 feet per second, while rifle bullets can travel at speeds of over 3000 feet per second. The exact speed also depends on factors such as barrel length, bullet weight, and gunpowder type.

3. How does the shape of a bullet affect its trajectory?

The shape of a bullet can greatly affect its trajectory. Bullets with a pointed tip, such as spitzer bullets, are more aerodynamic and experience less drag, resulting in a flatter trajectory. On the other hand, round-nosed bullets have more drag and tend to drop faster. The shape and weight of a bullet also affect its stability and accuracy in flight.

4. Can a bullet change direction after being fired from a gun?

Once a bullet is fired from a gun, it follows a straight path based on the initial velocity and trajectory. However, external factors such as wind, air density, and obstacles in the bullet's path can cause it to change direction. Additionally, some bullets are designed to have a slight curve in their path, known as a ballistic curve, for increased accuracy at longer distances.

5. How far can a bullet travel after being fired from a gun?

The distance a bullet can travel after being fired from a gun depends on various factors such as the type of gun, bullet weight, and angle of the shot. On average, a handgun bullet can travel up to 1-2 miles, while a rifle bullet can travel up to 3-5 miles. However, factors such as air resistance and gravity will cause the bullet to lose speed and drop to the ground before reaching these distances.

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