Question

You have five gears meshed to each other running in a line.the first gear Z=100,second, second gear Z =50,third gear Z=200,fourth gear Z =150 and fifth gear Z =200.the first gear turns clockwise at 100 revolutions per minute what direction will gear number 5 runs and at what speed

Answer 1

Answer:

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Answer 2

Given:

You have five gears meshed to each other running in a line. The first gear Z=100, second gear Z =50,third gear Z=200,fourth gear Z =150 and fifth gear Z =200.

To Find:

If the first gear turns clockwise at 100 revolutions per minute what direction will gear number 5 runs and at what speed?

Solution:

Since,  we know that -

When the number of intermediate gears are odd, the motion of both the gears (i.e. driver and driven or follower) is in like direction.

Therefore, here in our there are 5 gears are given and first gear turns clockwise, therefore, gear number 5 also turns in clockwise direction as intermediate gears are 3 (which is odd).

Now, to find speed of gear number 5, we have

$\dfrac{N_{1}}{N_{5}}=\dfrac{Z_{2}\times Z_{4}}{Z_{1}\times Z_{3}\times Z_{5}}$  

where, N is the speed of the gear and Z is the number of teeth in the gear.

given;

 $Z_{1}=100, \ Z_{2}=50 , \ Z_{3}=200 , \ Z_{4}=150 \ and \ Z_{5}=200\\N_{1}=100 \ r.p.m.$

On substituting the values , we get

$\dfrac{100}{N_{5}}=\dfrac{50\times150}{100\times200\times200}\\\\\\N_{5}=\dfrac{100\times2\times4\times200}{3}\\\\N_{5}=53344$

Hence, gear number 5 runs at the speed of 53344 r.p.m. in clockwise direction.