Newton's third law -- Calculate the recoil of a paintball gun

In summary, the problem involves finding the acceleration of a paintball gun with a mass of 5.5 kg after firing a paintball with a mass of 0.15 kg at a velocity of 45 m/s [N] for a duration of 0.10 s. Using Newton's second law, the acceleration of the paintball is calculated to be 450 m/s^2 [N], and the net force on the paintball is 68 N. The acceleration of the paintball gun is then found to be 12 m/s^2 by dividing the net force by the mass of the gun.
  • #1
Baran
11
3
Homework Statement
A paintball with a mass of 0.15 kg is fired from a paintball gun that has a mass of 5.5 kg. The paintball leaves the gun with a velocity of 45 m/s [N] having accelerated for 0.10 s. Calculate the acceleration of the paintball gun.
Relevant Equations
Givens:
Mass of paintball = 0.15 kg
Mass of paintball gun = 5.5 kg
initial velocity of paintball = 45 m/s [N]
time = 0.10 s
I've been stuck on this for sometime now, and am unsure how to approach this question.
 
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  • #2
Baran said:
Homework Statement:: A paintball with a mass of 0.15 kg is fired from a paintball gun that has a mass of 5.5 kg. The paintball leaves the gun with a velocity of 45 m/s [N] having accelerated for 0.10 s. Calculate the acceleration of the paintball gun.
Relevant Equations:: Givens:
Mass of paintball = 0.15 kg
Mass of paintball gun = 5.5 kg
initial velocity of paintball = 45 m/s [N]
time = 0.10 s

I've been stuck on this for sometime now, and am unsure how to approach this question.
First find the force on the paintball (hint: use Newton's second law).
 
  • #3
nrqed said:
First find the force on the paintball (hint: use Newton's second law).
I'm confused, in order to find the net force you would need acceleration, wouldn't you?
 
  • #4
Baran said:
I'm confused, in order to find the net force you would need acceleration, wouldn't you?
Yes, and you can calculate the acceleration. You know the speed of ejection and the time it took to accelerate the paintball.
 
  • #5
nrqed said:
Yes, and you can calculate the acceleration. You know the speed of ejection and the time it took to accelerate the paintball.
I think I got it:

a= vf-vi/t
a= 0 m/s- 45 m/s [N] / 0.10 s
a= -450 m/s^2 [N]
a= 450m/s

(this is the paintball)
Fnet= ma
Fnet= (0.15 kg) x(450 m/s^2 )
Fnet= 68 N

(this is the paintball gun)
Fnet= ma
a= Fnet/m
a= 68 N / 5.5 kg
a= 12 m/s^2

can you check if I did this right please?
(Sorry about the black lines I don't know how to fix that)
 
  • #6
looks good!
 
  • #7
nrqed said:
looks good!
Thanks for all your help!
 
  • Like
Likes berkeman and nrqed

1. What is Newton's third law?

Newton's third law states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will exert an equal force in the opposite direction.

2. How does Newton's third law apply to a paintball gun?

In the context of a paintball gun, Newton's third law means that when the gun fires a paintball, the paintball will exert an equal force on the gun in the opposite direction. This is what causes the gun to recoil or kick back when fired.

3. How can I calculate the recoil of a paintball gun?

To calculate the recoil of a paintball gun, you will need to know the mass of the paintball, the velocity at which it is fired, and the mass of the gun. Using the formula F=ma (force equals mass times acceleration), you can calculate the force of the paintball on the gun. This force will be equal to the force of the gun on the paintball, causing the recoil.

4. Does the mass of the paintball affect the recoil of the gun?

Yes, the mass of the paintball does affect the recoil of the gun. According to Newton's third law, the force of the paintball on the gun will be equal to the force of the gun on the paintball. This means that a heavier paintball will exert a greater force on the gun, resulting in a stronger recoil.

5. Are there any other factors that can affect the recoil of a paintball gun?

Yes, there are other factors that can affect the recoil of a paintball gun. These include the velocity at which the paintball is fired, the design and weight of the gun, and any external forces acting on the gun, such as wind or friction. These factors can all impact the amount of force exerted on the gun, and therefore, the recoil experienced.

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