i need help please on this mechincal question

You posted the exact same question 15 days ago. Nobody knew the answer then, what makes you think anybody knows it now? Ask your teacher if you can't understand your homework.

Re: i need help please on this mechincal question


by velocity ration, do you mean velocity ratio? and by velocity ratio, do you mean angular velocity ratio, because the linear velocity ratio is 1:1, which is a hint towards your answer.
For the question about the angle between the pulleys and the belt, draw it out on paper and get cracking with the mathematics.
For the maximum power, using the coefficient of friction is going to be key to finding your answer.

As for the merits of other systems, and other power transmission methods, you should have those in your textbook somewhere.

Give the man a break I too frequently type ration when I mean ratio

Answers

a) the larger pulley is turning at 5RPS , the smaller pulley has to be moving with the same face velocity--since the larger pulley circumperence is pi*500mm (C=pi*d) and the smaller pulley circumference is 150MM*Pi.

Then 5RPS*200mm*pi=S RPS*150mm*pi where S is the angular speed of the smaller pulley.

b) to get the pulley lap you have to use a little geometry---if you draw the two problems out you'll see that the lap of the larger pulley is slightly larger than 180 degrees and the smaller pulley is slightly smaller than 180 degrees. A little more thought will result that the difference between 180 degrees (more and less) over the two pulleys is equal (Symmetric)

Looking a little further---the difference between pulley centers is 600mm, and the diference in heights is the diference in pulley radii (r=d/2). The larger pulley is 200mm diameter (100mm) and the smaller pulley is 150mmm (75mm) the difference between the two is 25mm (100-75mm).

OK go back to your diagram of the two pulleys you'll see that this difference between the diameters and the distance between pulley centers now makes a right triangle, with a short leg of 25mm and a long leg of 600mm. A little more diagram analysis will show that the lap over a quarter of the larger pulley is 90 degrees plus the acute angle of this right triangle- This triangle is given by taking the arctangent of the short side (25mm) divided by the long side (600mm). Since a quarter is hale the lap then

Larger pulley lap=180+2ArcTan(25/600)

& Smaller pulley lap=180-2ArcTan(25/600)

c) Power transmission---

No slip=coefficient of friction*tension, or F=1K(ilo)Nt*0.25=250 Nt* face speed

Face Speed=Angular velocity*radius

Lets go with larger pulley(200mm) the radius is 100mm or 0.1m

The angular vvelocityis 5RPS*2*pi (radians/s)

Power is then (1Knt)*0.25*5 (rev/s) *2pi (rad/rev)*0.1 m=250*5*2*pi*.1 (nt m/s)=785 Nt m/s.

Being a 'Merican I like Horsepower or to be kind to Canuks--Kilowatts
785 Nt m/s = 1 .05 Hp
785 Nt m/s=785 watt= 0.785 Kw

d) other types of belts available?

The good old V-belt---workedfor years driving alternators, power steering and brake pumps, and AC compressors for millions of cars of past generations.

Toothed belt---works wonderful as the final drive of Harley Davidson motorcycles

e) other types of drives available---break the advantages and disadvantages of each into several categories----initial capital outlay (cost), difficulties in installation, mmaintainancerequired, and energy loss. Fortunatelythis isn't a real high power system (0.785 Kw isn't much power). So a flat belt is probably adequate--it's cheap, easy to install and maintain. But other systems to consider are the toothed belt (more efficient, requires a more careful installment and aalighment, bicycle chain (similar to the toothed belt), the v-belt (one of my particular favorites here--it's less likely to fly off the pulley than a flat belt and the cost & efficiency is equal or better), and geared transmission (not my favorite here)---it is very efficient, no slip, but kinda overkill and it requires a jack shaft gear to maintain direction so it will be very expensive.

Boy are you lucky---the normal fee for this kinda analysis is about $500---but then this isn't a formal report---and it hasn't been peer reviewed.

Rap

Is this what you do best Contrex