How does a hinged mass affect a catapult's launch time?

[ellaingeborg]

Homework Statement

Okay, so I am doing a physics investigation and I am supposed to have a theory I can test. I have a catapult I made myself, and I change the force exerted on the rod of the catapult by changing the mass that hangs by a string. It is a seesaw with a hinged mass on one end.
I am trying to find out how the mass affects the time of launch. How can I know what correlation they have?

Homework Equations

How do I create a theory about the correlation between the hinged mass and the time the rod takes to launch?

The Attempt at a Solution

I have tested it using different masses and my results showed that the larger the mass hanging by the string, the shorter the time of launch is. I believe this is because the tension of the string gets larger and thus the force that causes the catapults rod to rotate is. larger. I've tried to create some kind of equation that shows the relationship, but too many properties change in the catapult. If I increase the mass, I believe the acceleration increases, thus the speed. So how do I show a theoretical relationship between the mass and the time of launch?

 

[berkeman]

Homework Statement

Okay, so I am doing a physics investigation and I am supposed to have a theory I can test. I have a catapult I made myself, and I change the force exerted on the rod of the catapult by changing the mass that hangs by a string. It is a seesaw with a hinged mass on one end.
I am trying to find out how the mass affects the time of launch. How can I know what correlation they have?

Homework Equations

How do I create a theory about the correlation between the hinged mass and the time the rod takes to launch?

The Attempt at a Solution

I have tested it using different masses and my results showed that the larger the mass hanging by the string, the shorter the time of launch is. I believe this is because the tension of the string gets larger and thus the force that causes the catapults rod to rotate is. larger. I've tried to create some kind of equation that shows the relationship, but too many properties change in the catapult. If I increase the mass, I believe the acceleration increases, thus the speed. So how do I show a theoretical relationship between the mass and the time of launch?

Welcome to the PF.

You would start by drawing a Free Body Diagram (FBD) for each of the different parts of the mechanism and the projectile. Then you would use the summations of forces and moments to calculate the accelerations and velocities that result. Are you familiar with those calculations?

Can you post some pictures or diagrams of your apparatus?

 

[ellaingeborg]

Yes I have done this:

Welcome to the PF.

You would start by drawing a Free Body Diagram (FBD) for each of the different parts of the mechanism and the projectile. Then you would use the summations of forces and moments to calculate the accelerations and velocities that result. Are you familiar with those calculations?

Can you post some pictures or diagrams of your apparatus?

Yes so this is what I have:

where T is the tension, mg is the gravitational force and r is the length of the rod from the string to the pivot

I have already done the experiment where I investigate the effect a hinged mass has on the catapult. I have measured how different masses affect the final angular speed of the rod of the catapult and the time the catapult takes to launch. I need help finding a theory that could show the relationship between the mass and the time taken.

I know that the time taken for the mass to drop is the same amount of time the catapult takes to rotate its angle of rotation. I also know that the force causing the torque the catapult is the tension that comes from the string. My results showed that the time decreases as the mass increases, but they do not have a linear proportion according to my results.

How do I get to see what the relationship between the mass and the time is? There seem to be so many variables changing due to the mass and very few things seem to be constant which makes it difficult to find some kind of relationship between them.

I tried working something out by using the net force, F, acting on the mass which is
F=ma=mg-T.
T=m(g-a) and since I assume the acceleration is uniform,
a=d/t^2,
thus T=m(g-d/t^2).
But the tension of the string can't be constant since the force exerted on the rod gets larger as the mass increases, thus I don't know what to do.

 

[berkeman]

Yes I have done this:

Yes so this is what I have:

where T is the tension, mg is the gravitational force and r is the length of the rod from the string to the pivot

I have already done the experiment where I investigate the effect a hinged mass has on the catapult. I have measured how different masses affect the final angular speed of the rod of the catapult and the time the catapult takes to launch. I need help finding a theory that could show the relationship between the mass and the time taken.

I know that the time taken for the mass to drop is the same amount of time the catapult takes to rotate its angle of rotation. I also know that the force causing the torque the catapult is the tension that comes from the string. My results showed that the time decreases as the mass increases, but they do not have a linear proportion according to my results.

How do I get to see what the relationship between the mass and the time is? There seem to be so many variables changing due to the mass and very few things seem to be constant which makes it difficult to find some kind of relationship between them.

I tried working something out by using the net force, F, acting on the mass which is
F=ma=mg-T.
T=m(g-a) and since I assume the acceleration is uniform,
a=d/t^2,
thus T=m(g-d/t^2).
But the tension of the string can't be constant since the force exerted on the rod gets larger as the mass increases, thus I don't know what to do.

One important factor is that the angle the string makes with the lever arm changes as the lever arm rotates. This changes the torque applied by the mass to the lever arm. Can you include that angle in your calculations to see if that gives you a better match to your experimental results?