Quote:
Originally Posted by Samurai Let's consider a modified pipe. Attachment 1186027
This is a soild pipe, with a much strengthened center. Center is where the Superman is holding it. The thinner parts of the pipe will start twisting at 500Nm of torque, but the center won't twist until 2000Nm of torque.
If the human grip can be overcome with 50Nm and Superkid's grip requires 1000Nm to overcome, what happens when superman starts turning the center? I would say the Human side will start turning since the effective torque on that side is 50Nm (too less to twist the pipe). The superkid side of the pipe will be twisting because it can't handle above 500Nm of twisting force. This twist won't leak to the other side because the much bulkier center can easily withstand 500Nm of torque. Visualise, don't apply formulas.
If you still can't believe one side can rotate and other can twist... let's change the condition without changing the applied torque.
Let superman hold the center stationery. Let the human try to turn the pipe applying upto 50Nm. Let Superkid also try to turn the pipe, but he can go up to 1000Nm. As you can see effective torque everywhere is same as before. Now, the human side remains stationery, and the superkid side will twist once he exceeds 500Nm.
In the both the above cases, the human side will follow the superman (rotate or stationery), the superkid side will twist. |
@Samurai - I prefer visualisation rather than applying formulas too.
Let us make clear that when you use the word "rotate". It means that the shaft should reach a certain rpm say 50 rpm and go on rotating for a period of time say half hour.
There is difference between rotate and twist. Twisting of a shaft is only possible in some degrees say not more than 20 degrees. Beyond which any reasonable shaft will break.
Case I
Superman first applies 25 Nm to the centre. Nothing happens except a very small negligible twist (We can neglect this twist). The shaft as a whole is not rotating.
Super man now applies 51 Nm of torque, will the shaft rotate? No because for the shaft to rotate superman needs to apply 50 +1000= 1050 Nm.
Both the sides of the shaft will twist by a very small degree equivalent to the torque applied by superman.
The statement that twist in thinner portions of shaft will start only after 500 Nm is wrong. Twist is not like a diode which will start functioning once a threshold of 500 Nm is reached. Twist has a linear relation to the shaft.
The twist starts with even 0.5 Nm and it goes on increasing as you increase the applied torque.
But let us assume that a major chunk of the twist will happen only after 500 Nm as per your case. Consider it like a threshold as you have stated. So no twist before 500 Nm, to simplify things.
Coming back to the point
Super man now applies 500 Nm of torque. The end of pipe towards super kid starts twisting.
Say after 500 Nm of torque the shaft thin ends will twist 1 degree for 1 Nm.
501 Nm - Twist 1 degree.
502 Nm - Twist 2 degree.
.
.
.
This will go on till we reach 20 degree where the shaft will break.
The centre portion of the shaft has turned by 20 degree.
Same will be the turn in the shaft on the human end
as it it is attached firmly to the centre portion of the shaft which has only turned by 20 degree. The centre portion of the shaft cannot rotate now because we have applied only 520 Nm which is less than the total torque required to rotate the shaft ie. 1050 Nm.
So the shaft on the human side has rotated only 20 degree till now.
Now even if you even assume that the shaft can twist max to 720 degree (which is next to impossible as the shaft will break before that) then
500 Nm + 720 Nm (used for the 720 degree twist) = 1220 Nm which is higher than the required 1050 Nm the shaft should be already rotating by now.
Infact the centre portion of the shaft will rotate at 1050 Nm so shaft will start rotating at 1050 Nm where the super end kid of the shaft will be twisted by 1050-500= 550 degrees.
In Case II
Yes here the superkids side will twist but not rotate.
Are you getting confused between twist and rotate?