Machines B/C

[Nydauron]

I think you missed that it's a sphere and it's rolling, so we have to include rotational kinetic energy in our energy equation. Taking that into Consideration, We get [KE (translational) + KE (Rotational) = PE] The formula for rotational KE is (1/2 * Rotational Inertia * Omega^2 ). A solid sphere has a rpt. Inertia of (2/5) * Mass * (Radius^2) and Omega = V/R. Thus, we get the equation
(1/2) * M * V^2 + (1/2) * (2/5) *M * R^2 = M* G*H. Rearranging we get, v = sqrt((10/7)gh), giving us 8.5 m/s^2. This Presentation might help to understand this. Your turn!

Umaroth's solution is correct, the sphere has no reason to roll

Oh lol I forgot to say it was rolling. Ignore my stupidity

Sorry for stopping the flow, but I wanted to point out that that answer is still wrong.
When dealing with a ramp problem with a rolling sphere or cylinder, its easier to use the Parallel Axis Theorem. The reason is that if you set your pivot point as the contact point between the ball and the ramp, we can say the torque is only caused by the force of gravity on the sphere. Following this, we get a force diagram like this: https://i.imgur.com/vdR6dHH.png
When calculating moment of inertia, we use the Parallel Axis Theorem which states I_Total = md^2 + I_CoM
Where d is the distance between the pivot point and the center of mass and I_CoM is the moment of inertia of the object around its center of mass.
In the case of this problem I_CoM = 2/5 mr^2 and d = r. We plug in those values and we get I_Total = 7/5 mr^2.
We then continue the problem the same way as before.
mgh = 1/2 mv^2 + 1/2 I_Total*(v/r)^2
mgh = 1/2 mv^2 + 1/2 (7/5mr^2)(v/r)^2
gh = 1/2 v^2 + 7/10v^2
gh = 6/5 v^2
When you plug in the values, v = 6.45m/s. With sig figs, it rounds to 6m/s.
Please carry on with the question above.

[shrewdPanther46]

Umaroth's solution is correct, the sphere has no reason to roll

Oh lol I forgot to say it was rolling. Ignore my stupidity

Sorry for stopping the flow, but I wanted to point out that that answer is still wrong.
When dealing with a ramp problem with a rolling sphere or cylinder, its easier to use the Parallel Axis Theorem. The reason is that if you set your pivot point as the contact point between the ball and the ramp, we can say the torque is only caused by the force of gravity on the sphere. Following this, we get a force diagram like this: https://i.imgur.com/vdR6dHH.png
When calculating moment of inertia, we use the Parallel Axis Theorem which states I_Total = md^2 + I_CoM
Where d is the distance between the pivot point and the center of mass and I_CoM is the moment of inertia of the object around its center of mass.
In the case of this problem I_CoM = 2/5 mr^2 and d = r. We plug in those values and we get I_Total = 7/5 mr^2.
We then continue the problem the same way as before.
mgh = 1/2 mv^2 + 1/2 I_Total*(v/r)^2
mgh = 1/2 mv^2 + 1/2 (7/5mr^2)(v/r)^2
gh = 1/2 v^2 + 7/10v^2
gh = 6/5 v^2
When you plug in the values, v = 6.45m/s. With sig figs, it rounds to 6m/s.
Please carry on with the question above.

I think your solution is incorrect. When choosing the axis of rotation as the contact point, there are some complications. Avoiding the details, the torque about the contact point from the weight of the sphere does not necessarily imply that the ball must roll... it means that the angular momentum about the contact point should change (by definition T=dL/dt). If you do the math, I think you will realize that the apparent torque is "used up" by the orbital angular momentum of the ball about the contact point. There is a good section in Morin explaining this. If there was friction, the ball would roll.

If you just take the CM reference frame, you would see that theres no torque to make it roll.

[AlfWeg]

what is the ideal mechanical advantage of an Archimedes screw?

From replicacalliper: “ "Well if the inner radius of the screw is r, and the pitch is L, then I'd say d_in/d_out= √(L^2+(2πr)^2)/L"

Let’s get this marathon rolling again.

[madhavaniyengar]

Ok Alf lets get this rolling again with a question (courtesy of replicaacliper cuz we're all too lazy to think of one).


This crane is fixed at points A and B. Assuming all the girders are massless, find the magnitude of the force exerted on D by member BD in terms of W.

[smayya337]

Ok Alf lets get this rolling again with a question (courtesy of replicaacliper cuz we're all too lazy to think of one).


This crane is fixed at points A and B. Assuming all the girders are massless, find the magnitude of the force exerted on D by member BD in terms of W.

There's a very good chance this is wrong, but I got 525W/117

[madhavaniyengar]

Ok Alf lets get this rolling again with a question (courtesy of replicaacliper cuz we're all too lazy to think of one).


This crane is fixed at points A and B. Assuming all the girders are massless, find the magnitude of the force exerted on D by member BD in terms of W.

There's a very good chance this is wrong, but I got 525W/117

That's wrong. You should type out your work or thought process or something in case you were missing a key factor, idk.

[smayya337]

Ok Alf lets get this rolling again with a question (courtesy of replicaacliper cuz we're all too lazy to think of one).


This crane is fixed at points A and B. Assuming all the girders are massless, find the magnitude of the force exerted on D by member BD in terms of W.

There's a very good chance this is wrong, but I got 525W/117

That's wrong. You should type out your work or thought process or something in case you were missing a key factor, idk.

I think I found the issue... Is it 7W?
never mind

[madhavaniyengar]

There's a very good chance this is wrong, but I got 525W/117

That's wrong. You should type out your work or thought process or something in case you were missing a key factor, idk.

I think I found the issue... Is it 7W?
never mind

Yeah it isn't that. What method r u using?

[smayya337]

That's wrong. You should type out your work or thought process or something in case you were missing a key factor, idk.

I think I found the issue... Is it 7W?
never mind

Yeah it isn't that. What method r u using?

I have it at last - my equation was right, but my setup was not. It's 24W. Sorry for cluttering up the QM with failed attempts and happy new year to all of you!

[madhavaniyengar]

I think I found the issue... Is it 7W?
never mind

Yeah it isn't that. What method r u using?

I have it at last - my equation was right, but my setup was not. It's 24W. Sorry for cluttering up the QM with failed attempts and happy new year to all of you!

Happy new year and yeah thats right gj
I guess you ask a question now