Machines B/C

[oliviasl]

Okay, I'll guess I'll go since no one else is going.

1) Let's start easy: What are the three Archimedean simple machines?
2) A little harder: What is the ideal mechanical advantage of a 0.112in-40 UNC-3A x 0.5 screw? Explain what each of the numbers in the screw callout means.
3) In the diagram shown below, the block has a mass m = 100kg and there is a coefficient of friction μ = 0.203 between the surfaces on the top and bottom of the wedge. The angle of the wedge (between the two contact surfaces) is 15°. Assume every other surface is frictionless and the only moveable pieces are the wedge and the block. Calculate the force P required to raise the block.

Here's the answers I got:
1) Lever, screw, pulley
2) 0.112in refers to the major diameter. 40 means there are 40 threads per inch. UNC means the screw is a Unified National Coarse Thread screw. The 3 indicates the thread class, with 3 being the class with the lowest tolerance. "A "refers to external threads. The 0.5 means that the screw is half an inch long.
3) I got P = 687.7 N

[Ttonyxx]

Okay, I'll guess I'll go since no one else is going.

1) Let's start easy: What are the three Archimedean simple machines?
2) A little harder: What is the ideal mechanical advantage of a 0.112in-40 UNC-3A x 0.5 screw? Explain what each of the numbers in the screw callout means.
3) In the diagram shown below, the block has a mass m = 100kg and there is a coefficient of friction μ = 0.203 between the surfaces on the top and bottom of the wedge. The angle of the wedge (between the two contact surfaces) is 15°. Assume every other surface is frictionless and the only moveable pieces are the wedge and the block. Calculate the force P required to raise the block.

Here's the answers I got:
1) Lever, screw, pulley
2) 0.112in refers to the major diameter. 40 means there are 40 threads per inch. UNC means the screw is a Unified National Coarse Thread screw. The 3 indicates the thread class, with 3 being the class with the lowest tolerance. "A "refers to external threads. The 0.5 means that the screw is half an inch long.
3) I got P = 687.7 N

Yup! Everything is correct, your turn.

[RiverWalker88]

Revive?

Here's a problem I'd recommend for everyone that has some basic knowledge of trig (i.e. how the trig functions relate to a triangle) doing machines, as it really helps solidify and conceptualize the formula for IMA of a wedge (and you get the warm fuzzy feeling of having come up with something you can actually use during the event).

For both of the following wedges, the Ideal Mechanical Advantage can be described as . Using this, determine a formula for the IMA of both of these wedges in terms of the angle of the wedge . Wedge (a) is a right triangle, and wedge (b) is isosceles. Show and/or explain how you got your formula.

Machines QM Wedges.jpg (17.13 KiB) Viewed 2984 times

[Ttonyxx]

[/answer]_id=63182]
Revive?

Here's a problem I'd recommend for everyone that has some basic knowledge of trig (i.e. how the trig functions relate to a triangle) doing machines, as it really helps solidify and conceptualize the formula for IMA of a wedge (and you get the warm fuzzy feeling of having come up with something you can actually use during the event).

For both of the following wedges, the Ideal Mechanical Advantage can be described as . Using this, determine a formula for the IMA of both of these wedges in terms of the angle of the wedge . Wedge (a) is a right triangle, and wedge (b) is isosceles. Show and/or explain how you got your formula.


Machines QM Wedges.jpg

I agree, this becomes pretty useful in competition. Here's my solution:

Click to Show Answer

[RiverWalker88]

[/answer]_id=63182]
Revive?

Here's a problem I'd recommend for everyone that has some basic knowledge of trig (i.e. how the trig functions relate to a triangle) doing machines, as it really helps solidify and conceptualize the formula for IMA of a wedge (and you get the warm fuzzy feeling of having come up with something you can actually use during the event).

For both of the following wedges, the Ideal Mechanical Advantage can be described as . Using this, determine a formula for the IMA of both of these wedges in terms of the angle of the wedge . Wedge (a) is a right triangle, and wedge (b) is isosceles. Show and/or explain how you got your formula.


Machines QM Wedges.jpg

I agree, this becomes pretty useful in competition. Here's my solution:

Click to Show Answer

Looks great for wedge B! Wedge A is a little different (not sure if you just missed it or...?)

And yeah, I did the derivation a couple of times and the formula is completely solidified in my head–again would recommend trying this out to anyone who does Machines.

[Ttonyxx]

[/answer]_id=63182]
Revive?

Here's a problem I'd recommend for everyone that has some basic knowledge of trig (i.e. how the trig functions relate to a triangle) doing machines, as it really helps solidify and conceptualize the formula for IMA of a wedge (and you get the warm fuzzy feeling of having come up with something you can actually use during the event).

For both of the following wedges, the Ideal Mechanical Advantage can be described as . Using this, determine a formula for the IMA of both of these wedges in terms of the angle of the wedge . Wedge (a) is a right triangle, and wedge (b) is isosceles. Show and/or explain how you got your formula.


Machines QM Wedges.jpg

I agree, this becomes pretty useful in competition. Here's my solution:

Click to Show Answer

Looks great for wedge B! Wedge A is a little different (not sure if you just missed it or...?)

And yeah, I did the derivation a couple of times and the formula is completely solidified in my head–again would recommend trying this out to anyone who does Machines.

Oh yeah whoops forgot about wedge A

Click to Show Answer

[RiverWalker88]

I agree, this becomes pretty useful in competition. Here's my solution:

Click to Show Answer

Looks great for wedge B! Wedge A is a little different (not sure if you just missed it or...?)

And yeah, I did the derivation a couple of times and the formula is completely solidified in my head–again would recommend trying this out to anyone who does Machines.

Oh yeah whoops forgot about wedge A

Click to Show Answer

Yep, looks great! Your turn!

[Ttonyxx]

1) What is the machine below called?

2) Derive the mechanical advantage formula for this machine and explain each step in your own words (not just taken from Wikipedia) .
3) If R is 50cm and r is 37cm, what F is needed to lift a 50kg object using this machine?

[ScoutViolet]

1:

Click to Show Answer

(Weston's) differential Pulley Block

2:

Click to Show Answer

The IMA is 2 times large radius divided by (Large Radius-Small Radius). (In my notes)

3:

Click to Show Answer

well 100/13 is the IMA, 50/(100/13)=50 times 13/100=13/2=6.5 kg, which is about 63.7N

[Ttonyxx]

1:

Click to Show Answer

(Weston's) differential Pulley Block

2:

Click to Show Answer

The IMA is 2 times large radius divided by (Large Radius-Small Radius). (In my notes)

3:

Click to Show Answer

well 100/13 is the IMA, 50/(100/13)=50 times 13/100=13/2=6.5 kg, which is about 63.7N

Great! For number 2, I was expecting more of a complete derivation, but that's fine. Your turn!