Torque and power in a geared sytem

[jmiersy]

Homework Statement

The problem is attached, I am only looking for guidance on a, I am most probably just completely over complicating this.

Homework Equations

p=T.2(pi).f

t= torque
f=frequency/rot/sec

The Attempt at a Solution

im just stuck on wether the power in shaft b is simply 95percent of the systems input power, or wether i calculate the torque in shaft a, and then calcualte the power in b and subtract a 5 percent from that. Thats what i tried however I got a power higher then the input. Please help.

 

[jmiersy]

p.s. thanks in advance.

 

[jmiersy]

so I am leaning towards the idea that power is simply .95 percent of the power supplied, meaning that the angular velocity and the torque are obviously different. am i on the right track of understanding this?

 

[jmiersy]

so assuming that this is correct, i then attempted b.
it asks for max torque in shaft b, max torque occurs at max power.
max power occurs when 2444 rpm.
40/208 = .1923 rotations to every one of the small gear
x by 2444
/60
= 7.8 rots/sec of the large gear.
so
p=T.2(pi).f
28.5x10^3=T.2(pi).7.833
T=579.07 nm

does this look correct?

thanks for input.

 

[DeeNos]

As a scientist, it is important to carefully consider all factors in a problem before arriving at a solution. In this case, it is necessary to understand the relationship between torque and power in a geared system. Torque is a measure of the rotational force applied to an object, while power is the rate at which work is done. In a geared system, the torque is multiplied by the gear ratio, while the power remains the same.

To solve this problem, it is important to first calculate the torque in shaft A. This can be done by using the equation T= P/2(pi)f, where P is the power and f is the frequency in rotations per second. Once the torque in shaft A is determined, the gear ratio can be used to calculate the torque in shaft B.

Next, the power in shaft B can be calculated by using the equation P=T(2(pi)f), where T is the torque and f is the frequency. This will give the total power in shaft B. However, since the question specifies that the power in shaft B is only 95% of the input power, it is necessary to multiply the calculated power by 0.95 to get the actual power in shaft B.

In summary, to accurately calculate the torque and power in a geared system, it is important to consider the gear ratio and the specified percentage of power in the output shaft. By carefully applying these equations and considering all factors, a more accurate solution can be obtained.