EK 1001 lever problems with self made pic!

[GRod18]

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So hopefully these are the last problems I will have with simple machines and mechanical advantage, Always thought this was an easy topic but EK problems are killing me!


457-458 refer to the three type of levers shown below: each lever stick is one meter long and massless. The triangle beneath each lever represents the fulcrum. The black dot represents the point 25 cm from the right end of the lever stick.

I just want to hear how you guys would reason through something like this. Intuition or math would be helpful.

457. If the same force F is applied through 10 cm by each lever, which lever lifts the mass to the greatest height?
Answer Y only.

458. If same force F is applied through 10 cm by each lever, which lever gives the mass the greatest final velocity?
Answer Z only.

Thanks in advance!

 

[fizzgig]

457. all of the forces do cause the mass to move upward (always do that kind of sanity check. the mcat loves making an ass out of us). if i move a point on the board through a 10cm arc length, points closer to the fulcrum on the board will move less than 10cm, points farther out on the board will move more than 10cm. so the answer to this should be whichever picture has the mass farthest from the rotation point.

458. this is more directly asking about the concept of mechanical advantage. i think you should look at these as sum of torques kind of problems. mechanical advantage means you can apply less force to move stuff. you want the picture with the highest advantage/least force required, the one that is easiest to accelerate. Y looks pretty bad. intuitively that one seems like it would be difficult - you get the most bang for your buck in terms of DISTANCE you move the point where you apply your force (it moves the mass the most) but it is harder to move, requires a larger minimum force. X and Z seem more likely. look at the torques you'd have for these.
X -> 75cm*F = 25cm*mg --> F=1/3mg
Z -> 100cm*F = 25cm*mg-->F=1/4mg
these are the forces required to just keep the block stationary. Z requires less force, it will be easier to move, higher acceleration. since in Z and X the mass is the same distance from the rotation point, a higher angular acceleration means higher velocity.

hope there's some sense in there.

 

[GRod18]

457. all of the forces do cause the mass to move upward (always do that kind of sanity check. the mcat loves making an ass out of us). if i move a point on the board through a 10cm arc length, points closer to the fulcrum on the board will move less than 10cm, points farther out on the board will move more than 10cm. so the answer to this should be whichever picture has the mass farthest from the rotation point.

458. this is more directly asking about the concept of mechanical advantage. i think you should look at these as sum of torques kind of problems. mechanical advantage means you can apply less force to move stuff. you want the picture with the highest advantage/least force required, the one that is easiest to accelerate. Y looks pretty bad. intuitively that one seems like it would be difficult - you get the most bang for your buck in terms of DISTANCE you move the point where you apply your force (it moves the mass the most) but it is harder to move, requires a larger minimum force. X and Z seem more likely. look at the torques you'd have for these.
X -> 75cm*F = 25cm*mg --> F=1/3mg
Z -> 100cm*F = 25cm*mg-->F=1/4mg
these are the forces required to just keep the block stationary. Z requires less force, it will be easier to move, higher acceleration. since in Z and X the mass is the same distance from the rotation point, a higher angular acceleration means higher velocity.

hope there's some sense in there.

ah IC so 457 is like a trebuchet kind of a deal right?

458 makes perfect sense thanks!

 

[fizzgig]

the way i recall trebuchets being set up i'd say X's setup is more like it, except the relative lever arms of the force and block you're gonna throw are switched... catapults use gravity on both sides.

Y is more like... just where an idiot would try to lift that thing 🙂 or a short person, i suppose...