Simple Machines B/Compound Machines C

[Shreyas1030]

For Div B how fast are you guys finding the ratios for the 3 masses? My partner and I were able to find the ratios in about 30secs to 1 minute at our most recent competitions. I think it's pretty slow. . In all competitions we've gone to, almost all the teams have dominated in the test portion. Therefore, our machine score is very crucial. Our machine is extremely accurate we just want to go faster. What do you guys think? What time should I be aiming for?

[Unome]

For Div B how fast are you guys finding the ratios for the 3 masses? My partner and I were able to find the ratios in about 30secs to 1 minute at our most recent competitions. I think it's pretty slow. . In all competitions we've gone to, almost all the teams have dominated in the test portion. Therefore, our machine score is very crucial. Our machine is extremely accurate we just want to go faster. What do you guys think? What time should I be aiming for?

30 seconds is good; with good accuracy you should be getting scores near 45-48. Test portion helps a lot though.

[slytherin]

For Div B how fast are you guys finding the ratios for the 3 masses? My partner and I were able to find the ratios in about 30 secs to 1 minute at our most recent competitions. I think it's pretty slow. . In all competitions we've gone to, almost all the teams have dominated in the test portion. Therefore, our machine score is very crucial. Our machine is extremely accurate we just want to go faster. What do you guys think? What time should I be aiming for?

Haha, my partner and I rock the test and were eh in the ratios, we realized our machine got a little off though so we fixed that and now we got a ratio .03 and .1 off in around 40 seconds I think..

[PLP Sci Oly]

The rulebook states any calculator can be used. Does this include calculators or calculator apps found on phones?, or does this mean any calculator with physical buttons?

[blindmewithscience]

The rulebook states any calculator can be used. Does this include calculators or calculator apps found on phones?, or does this mean any calculator with physical buttons?

Of course, this isn't the place for official rule clarifications. But regarding phone usage, here's a quote from the general rules:

All electronic devices capable of external communication (including cell phones) must be turned off, unless expressly permitted in the event rule and left in a designated spot if requested.

So my interpretation is that you're not allowed to use any phone calculator at all in this event. In addition, I'd assume that any normal calculator that you could use in a math class could be used in this event, as the rules state

and any type of calculators for use during both competition parts. Calculators do not need to be impounded.

What's your desire to use a phone calculator? Nearly all physical calculators are easier to use, have a readable memory, and many are programmable as well, such as the TI-84 (which can help you in the competition).

[PLP Sci Oly]

Thank you for the clarification! You do give good points though. We were planning on using a calculator app with equation memory instead of a new calculator, but I guess we will need one anyways. Again, thank you for your help.

[TrueshotBarrage]

The left lever is pushing upwards on the right lever at the point of contact.If we look at the left lever alone, what mass would need to be on the other side of the lever to have it at equilibrium? From the equation, we get m=Y*d1/d2.
The right lever is pushing downwards on the left lever at the point of contact. If we look at the right lever alone, what "mass" would need to be pushing upwards on the right lever? From the equation, we get n=R*d4/d3
Now, these two "masses" are equal (this comes from newtons third law, if we simply turn them into forces).so, we get that Y*d1/d2=R*d4/d3. Solving, the ratio Y/R=d4*d2/(d3*d1).
Now the best part of this equation is that d2 and d3 can be measured in advance, and you simply have to plug in your distances.
I'm pretty tired right now (school and stuff) so please correct me if I made a mistake.

Hello, thanks for the awesome drawing! It definitely helped me understand the concept of the levers better.

Where you say m and n, what exactly are you referring to? I'm assuming that the variables are the unknown masses, but I'm not sure, since you said Y and R.

Also, I'm pretty confused on how you can already know d2 and d3 from the start. If you knew those, wouldn't you know d1 and d4 as well?

Just general clarification from anyone would be awesome. Thanks, and thanks again for understanding I'm a noob at this event (and Div C in general)!

[bernard]

The left lever is pushing upwards on the right lever at the point of contact.If we look at the left lever alone, what mass would need to be on the other side of the lever to have it at equilibrium? From the equation, we get m=Y*d1/d2.
The right lever is pushing downwards on the left lever at the point of contact. If we look at the right lever alone, what "mass" would need to be pushing upwards on the right lever? From the equation, we get n=R*d4/d3
Now, these two "masses" are equal (this comes from newtons third law, if we simply turn them into forces).so, we get that Y*d1/d2=R*d4/d3. Solving, the ratio Y/R=d4*d2/(d3*d1).
Now the best part of this equation is that d2 and d3 can be measured in advance, and you simply have to plug in your distances.
I'm pretty tired right now (school and stuff) so please correct me if I made a mistake.

Hello, thanks for the awesome drawing! It definitely helped me understand the concept of the levers better.

Where you say m and n, what exactly are you referring to? I'm assuming that the variables are the unknown masses, but I'm not sure, since you said Y and R.

Also, I'm pretty confused on how you can already know d2 and d3 from the start. If you knew those, wouldn't you know d1 and d4 as well?

Just general clarification from anyone would be awesome. Thanks, and thanks again for understanding I'm a noob at this event (and Div C in general)!

The rules say you need a class 1 and class 2 lever, each no more than 40 centimeters (for the class 1 that is the distance from load to effort, and for class 2 it is the distance from the fulcrum to the effort). You know d2 and d3 because they are always the same. d2 is the distance from the fulcrum of the class 1 lever to the right end of the lever (which depends on how your device is made). For our device, it is about 20 cm because I placed the fulcrum exactly in the middle of the 40 cm lever. Same thing for d3, which is the distance from the fulcrum of the class 2 lever to the left end of it, but for our device d3 is 40 cm, the maximum allowed length for the lever.

Now, d1 and d4 are unlike d2 and d3. d1 and d4 are distances from the point of the load to the fulcrum. To determine the ratio of your masses, you would hang them and shift them left and right until both levers are horizontal (if you made your device like the one shown). Depending on the masses, the positions of these masses that give you this equilibrium will vary, so d1 and d4 will vary. d1 is the distance from the load of the mass labeled "Y" to the fulcrum of the class 1 lever, and d4 is the distance from the load of the mass labeled "R" to the fulcrum of the class 2 lever.

I'll go through the math again in another reply. I just tried to go through the math again and realized that the diagram posted isn't the easiest setup (you would want a rigid connection between the two levers since the class 2 lever appears to be above the class 1 lever. I'll post a picture of our team's device along with my explanation.

[bernard]

I don't feel like getting our team's device to take a picture of it or making another diagram so I'll just make some corrections to the diagram already posted. Take the lever on the right (the class 2 lever) and shift it down so the lever is under the lever on the left (the class 1 lever). Now imagine a string joints the closest two ends of the levers (that would be the right end of the class 1 lever and the left end of the class 2 lever).



When I put a mass on the left side of the class 1 lever, it causes the side to the right of the fulcrum to go up. Forces involved are the downwards gravitational force of the mass, Y, and the force of the right side going up and pulling up the left side of the class 2 lever. When I put a mass on the left side of the fulcrum of the class 2 lever, this causes the left side to go down, which also pulls down on the right side of the class 1 lever. By Newton's third law, the force of the right side of the class 1 lever pulling up on the string and the force of the left side of the class 2 lever pulling down on the string are equal. Let's call this force F. (In the equations posted by the other user, m and n both represent F, which is pointed out with Newton's third law.) We can get these equations: Y * d1 = d2 * F and F * d3 = R * d4.

Let's solve for F in both equations: F = Y * d1 / d2 and F = R * d4 / d3. Equating these two gives us Y * d1 / d2 = R * d4 / d3. Solving for Y / R gives us Y / R = (d4 * d2) / (d1 * d3). As I said in my previous post, d1 and d4 are constant, so those can be substituted and you have a simple formula you can use during testing.

I'll post my pictures later, maybe tomorrow evening.

[GoldenKnight1]

Also, I'm pretty confused on how you can already know d2 and d3 from the start. If you knew those, wouldn't you know d1 and d4 as well?

Just general clarification from anyone would be awesome. Thanks, and thanks again for understanding I'm a noob at this event (and Div C in general)!

The rules say you need a class 1 and class 2 lever, each no more than 40 centimeters (for the class 1 that is the distance from load to effort, and for class 2 it is the distance from the fulcrum to the effort). You know d2 and d3 because they are always the same. d2 is the distance from the fulcrum of the class 1 lever to the right end of the lever (which depends on how your device is made).

You don't have to know d2 and d3 from the start if you decide to make the connection point between the two levers variable. While many teams keep these points fixed so that d2 and d3 would be constant it is not necessary. Also many devices I have seen have rotated the 2nd class lever and increased the length of the material connecting the two levers together so that the levers are stacked on top of each other or at right angles. I am not saying which is better or worse. Each have their own advantages.