# Proportionality theorem and projectile motion

• LT72884
In summary: This gives you the distance/frame rate.In summary, you can approximate the velocity of a mass using the stopwatch method and the distance traveled between two subsequent frames.
LT72884
So i have this question. If a projectile is fired from a spring loaded system and when it goes pass a chronograph, reads 300FPS and has a mass of 0.12grams. Is there any way to use the proportionality theorem (1/3=x/6 example) to approximate how fast a mass of 0.25grams is when fired from same system? I know it SHOULD be slower. Nothing is know about the system, no spring force, no acceleration etc. All i have is mass and fps of the projectile.

thanks. i know its an odd question. I just want to know if there is a proportionality theorem that would work haha

LT72884 said:
If a projectile is fired from a spring loaded system and when it goes pass a chronograph, reads 300FPS and has a mass of 0.12grams. Is there any way to use the proportionality theorem (1/3=x/6 example) to approximate how fast a mass of 0.25grams is when fired from same system?
The energy in the spring the same. So if you assume that it all goes into kinetic energy of the projectile, the projectile velocity will be inversely proportional to the square root of the projectile mass.

This is ignoring spring inertia, which becomes relevant if the projectile mass becomes relatively small.

A.T. said:
The energy in the spring the same. So if you assume that it all goes into kinetic energy of the projectile, the projectile velocity will be inversely proportional to the square root of the projectile mass.

This is ignoring spring inertia, which becomes relevant if the projectile mass becomes relatively small.
ok, that makes sense. Would you be willing to put that into an equation for me. I want to calculate the velocity to see if i want to purchase the spring loaded system. Thanks

A.T. said:
So if you assume that it all goes into kinetic energy of the projectile

How do you justify this assumption if nothing is know about the system?

DrStupid said:
How do you justify this assumption if nothing is know about the system?
By assuming a massless spring and no damping, since the OP asks for a simple relation.

A.T. said:
By assuming a massless spring and no damping, since the OP asks for a simple relation.

The problem is that a massless spring is very theoretic whereas the question sounds quite practical. With your assumption you might get a lower limit for projectiles with higher mass. But I expect it to fail for lower mass projectiles. It would be helpful if we would have data for at least two projectiles with different mass. Than we wouldn't need to guess.

DrStupid said:
The problem is that a massless spring is very theoretic whereas the question sounds quite practical. With your assumption you might get a lower limit for projectiles with higher mass. But I expect it to fail for lower mass projectiles.
I agree. For very light projectiles their mass differences become irrelevant, as they all shoot out at the same velocity, determined by the spring parameters.

yeah, i only got the one number off the package. 300fps with a 0.12g bb. I have 0.25g bb's so i know fps will be lower, but i don't have a chrono graph, and trying to calculate by hand with a crapy stop watch and distance marker sucks haha.

thanks

LT72884 said:
i don't have a chrono graph, and trying to calculate by hand with a crapy stop watch and distance marker sucks haha.
Many mobile phones and consumer cameras have a slowmo mode (high frame rate). You can measure the distance traveled between two subsequent frames and divide by the frame duration.

## 1. What is the Proportionality Theorem?

The Proportionality Theorem, also known as the Triangle Proportionality Theorem, states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally.

## 2. How is the Proportionality Theorem used in projectile motion?

In projectile motion, the Proportionality Theorem is used to determine the relationship between the distance traveled horizontally and the height reached vertically by a projectile. This helps in calculating the trajectory and range of the projectile.

## 3. What is the difference between horizontal and vertical motion in projectile motion?

Horizontal motion refers to the movement of a projectile in the x-axis, while vertical motion refers to its movement in the y-axis. In projectile motion, these two motions are independent of each other, meaning the horizontal velocity remains constant while the vertical velocity is affected by gravity.

## 4. How does air resistance affect projectile motion?

Air resistance, also known as drag, can affect the motion of a projectile by slowing it down and changing its trajectory. This is because air resistance acts in the opposite direction of the projectile's motion, reducing its speed and altering its path.

## 5. What are some real-life examples of projectile motion?

Some common examples of projectile motion in everyday life include throwing a ball, shooting a basketball, and launching a rocket into space. Other examples include a baseball being hit by a bat, a bullet being fired from a gun, and a water balloon being thrown.

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