Question

Please help:
a gun with a barrel of .63 meters fires a bullet that has a muzzle velocity of 250 m/s. The mass of the bullet is 0.025 kg. What is the force acting on the bullet while it is in the barrel of the gun? If the gun accelerated backward at a rate of 0.75 m/s^2, what is its mass?

Answer 1

alright lets look at the bullet first, and we are just going to try and figure it out with the units before we do the math. So we know we need to figure out a force so we can apply newton's 3rd law to the gun. We know that force is measured in newtons so lets break down that unit and see what we can come up with.

\[N= Kg*\frac{m}{s^2}\]

Answer 2

So we have a Kg but a lacking a acceleration so I checked out the kinematic equation's and think I found one we have the information to solve for acceleration.

\[V_f^2=V_i^2+2ad\]

Answer 3

Now that we have an acceleration for the bullet we can use the general equation F=ma to calculate the mass of the gun.

\[m_{gun}a_{gun}=m_{bul}a_{bul} \rightarrow m_{gun}=\frac{m_{bul}a_{bul}}{a_{gun}}\]

Answer 4

Then you can check the units

Answer 5

okay, so can you use Fg=mg for the first step to solve this?

Answer 6

Or Fnet=ma

Answer 7

or the acceleration/ velovity equation?

Answer 8

sorry, it is because I don't think we have learned the kinematic equation.

Answer 9

We have gone over Newtons 1-3 laws

Answer 10

I would use the kinematic equation because it asks for the force acting on the bullet inside the barrel.

Answer 11

ohh wait, my bad.. we have used the kinematic equions, I just wasnt aware it was called that

Answer 12

the first equation you are talking about is the Kg/(m/s^2)= N .. Right?

Answer 13

no Kg* (m/s^2)=N

Answer 14

okay for acceleration I plugged in 250^2=0^+2a(.63)

Answer 15

is that right?

Answer 16

yes that looks right

Answer 17

okay then I got 99206
then I plugged it into kg(m/s^2)
.025(99206)= 2480N

Answer 18

so far so good?

Answer 19

@zbay

Answer 20

you should get a number like 1240n

Answer 21

divide thatby the acceration of the gun and you get the mass of the gun

Answer 22

wait, how did you get 1240?

Answer 23

@zbay

Answer 24

I used the kinematic equation to find acceleration then multiplied it by the the mass of the bullet.

Answer 25

which is what I did, but I got 2480

Answer 26

Did you multiply (.025*99206)?

Answer 27

@zbay

Answer 28

ohhh, is it 1240 because tht is the force of one of the forces, not both of the forces added together?

Answer 29

okay so what do you do after you get 1240?

Answer 30

the 1240 is both of the forces due to the newton's 3rd law

Answer 31

okay, so did I multiply the right numbers? (.025)(99206)?

Answer 32

@zbay

Answer 33

you are messing up with the calculator somewhere you should end up with .025(49603)

Answer 34

to be more detailed it would be
F=.025(4903)

Answer 35

ahh, yes you are right, I messed up earlier in the roblem with my calculator, srry.. okay so what do I d after that?

Answer 36

\[a=\frac{250^2}{.63(2)}\]

Answer 37

mass=1403/.75

Answer 38

okay, so tht would be the mass of??

Answer 39

the gun it seems rather heavy but the math should be right

Answer 40

okay.. so then what would be the next step?

Answer 41

thats it you were looking for the mass of the gun

Answer 42

oh yes.. oky thank you very much! just one more question, if we were to draw a force diagram, what would the force acting on the bullet while it is in the barrel be NAMED?

Answer 43

@zbay

Answer 44

do you understand what I am trying to say? do you need me to clarify?

Answer 45

i'm not sure

Answer 46

do you know how the force diagram would look like?

Answer 47

no sorry

Answer 48

Alright, its ok.. thank you so much for ALL your help! im sorry it took me a while but I really appreciate it, thanks(: