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

AI Thread Summary
To calculate the recoil of a paintball gun using Newton's third law, the mass of the paintball (0.15 kg) and the gun (5.5 kg) are considered. The paintball is ejected at a velocity of 45 m/s over 0.10 seconds, allowing for the calculation of its acceleration as 450 m/s². The net force on the paintball is determined to be 68 N, which is then used to find the acceleration of the paintball gun, resulting in 12 m/s². The calculations are confirmed to be correct, demonstrating the application of Newton's laws in this scenario. Understanding these principles is essential for solving similar physics problems.
Baran
Messages
11
Reaction score
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.
 
Physics news on Phys.org
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).
 
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?
 
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.
 
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)
 
looks good!
 
nrqed said:
looks good!
Thanks for all your help!
 
  • Like
Likes berkeman and nrqed
Back
Top