The speed of a bullet may be determined by allowing the bullet to pass throu

In summary, the speed of a bullet can be determined by allowing it to pass through two rotating paper disks mounted a distance d apart. By using the angular displacement Δθ of the two bullet holes in the disks and the rotational speed of the disks, the speed of the bullet can be calculated using the equation v = d/Δt. In the given problem, the bullet speed is approximately 139 m/s.
  • #1
XxBollWeevilx
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[SOLVED] The speed of a bullet may be determined by allowing the bullet to pass throu

Hello! I am new here and this is my first time posting...I am working on a physics problem and I have been stumped on it for a while now. Any hints would be greatly appreciated.

Homework Statement



The speed of a moving bullet can be determined by allowing the bullet to pass through two rotating paper disks mounted a distance d apart on the same axle. From the angular displacement Δθ of the two bullet holes in the disks and the rotational speed of the disks, we can determine the speed v of the bullet. Find the bullet speed for the following data:

d=80 cm, ω=900 rev/min, and Δθ=31º.

Homework Equations



My initial thought was that I would need to use the rotational kinematics formulas in some way or another:
1. ω = ω(initial) + αt
2. θ = θ(initial) + 1/2(ω + ω(initial))t
3. θ = θ(initial) + ω(initial)t + 1/2αt^2
4. ω^2 = ω(initial)^2 + 2α(θ - θ(initial))

to somehow get t, and then use the horizontal displacement over t to find v, the velocity of the bullet.


The Attempt at a Solution


Some of my thoughts: I do not know what alpha, the angular acceleration is, so I cannot use it in order to find t. This rules out equations 1, 3, and four, leaving me with equation 2 to work with. Only one angular velocity was given in the problem, so the omegas in the formula confuse me, and I'm not sure if I need to use the same number for omega initial and omega final, or if I am supposed to assume constant angular velocity at all. If so, I think I can use 0 as theta initial and the 31 degrees as theta final to find t.

If this is in fact the correct way to approach this problem (I have searched the chapter in the book and can't seem to find another approach), the last thing on my mind is the issue of radians and degrees. Should I change every aspect of the problem to radians, or to degrees? My initial impression was radians, but from the way I'm looking at it, I'm not sure if it would make a difference, or if there is a correct way to do this. I am again assuming that the velocity remains constant, so that is how I can find it, by dividing d by time.

ANY hint or small tip in the right direction would be greatly appreciated. Thanks ahead for any help.
 
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  • #2
Some of my thoughts: I do not know what alpha, the angular acceleration is
well, from the problem statement, I will conclude that the discs are rotating with constant angular velocity, so alpha is zero.
 
  • #3
Try to understand this: (my english is poor, sorry for that)

The first disc rotated by 31 degrees in the same time as the bullet took to travel 80 cm.

omega of disc(which will be constant) =900x(2xpi)/60 rad/sec. (pi=3.14)

convert 31 degrees into rad by multiplying by (pi/180). = 31x (3.14/180)

time taken by disc to rotate 31 degree = (31x(3.14/180) / omega) seconds

this time =0.80/v.

____________________________________
I may be wrong...
 
Last edited:
  • #4
Thanks so much for the help! Here's what I did and how I got it:

First converted d into meters, 80 cm = 0.80m
Converted omega into rad/s, 900 rev/min(1 min/60 s)(2pi/1 rev) = 94.2 rad/s
Converted degrees into radians (like you said), 31 degrees(pi/180 degrrees) = 0.541 rad


Then I used equation 3 from above...theta initial and alpha are both zero, so I just took 0.541 rad / 94.2rad/s to get 5.74x10^-3 s for t (0.00571 s)

Then I took 0.80m/0.00571s = 139 m/s

How does this look, and thanks so much for the help!
 
  • #5
Again, I'm pretty sure that it looks right.
 
  • #6
Bump...sorry if we're not allowed to bump.
 
  • #7
do an order of magnitude estimate
disks 1m apart, rotate in 1/15 seconds hits are 1/6 of a turn apart = 0.01s
so answer is roughly 100m/s
You have made things slightly complicated for yourself with radians etc.

That isn't actually realistic for anything other than a musket ball - but you never know how accurately the question was set!
 
  • #8
Thanks...but is it still suitable, the way I did it in radians? So far, everything we've learned in class has been in radians for objects rotating about a fixed axis.
 
  • #9
A bit unnecessary but the right answer.
 
  • #10
OK...thank you so much for the assistance, I really appreciate it.
 

Related to The speed of a bullet may be determined by allowing the bullet to pass throu

What is the speed of a bullet?

The speed of a bullet can vary depending on several factors such as the type of gun, the type of bullet, and the environmental conditions. On average, a bullet can travel at speeds of 1,500 feet per second or more.

How do you determine the speed of a bullet?

There are several methods to determine the speed of a bullet, including using a chronograph, which measures the time it takes for a bullet to pass through two sensors, or using high-speed cameras to capture the bullet's movement.

Does the speed of a bullet change as it travels?

Yes, the speed of a bullet can change as it travels due to various factors such as air resistance, gravity, and friction. However, the change in speed is usually minimal and does not significantly affect the overall velocity of the bullet.

What is the fastest recorded speed of a bullet?

The fastest recorded speed of a bullet is approximately 4,000 feet per second, achieved by a .220 Swift rifle. However, the speed of a bullet can vary greatly depending on the gun and bullet used.

Can the speed of a bullet be increased?

It is possible to increase the speed of a bullet by using a more powerful gun or a lighter and more aerodynamic bullet. However, there may be legal restrictions on the maximum speed of a bullet in certain areas.

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