is this the right approach, pls help

[getinthere]

in a V belt drive the ratio of the belt tensions at the limiting value
of friction is governed by the following equation:

T=Toe<sup>u(x/sina)

calculate the V belt semi angle (a) given that:
The tension in the loaded part of the belt, T is 302 Newtons

The tension in the unloaded part of the belt To is 0.43 T

The coefficient of friction u is 0.3

The angle of lap is 148 deg

302=0.43ln^0.3(148/sina)

302/0.43=ln^0.3(148/sina)

ln(302/0.43)=0.3(148/sina)

0.3(ln)(302/0.43)=148/sina

148(0.3)(ln)(302/0.43)=sina

sina =291.0152307

im stuck if this is not right and would love some help if i need it thanks</sup>

 

[HallsofIvy]

in a V belt drive the ratio of the belt tensions at the limiting value
of friction is governed by the following equation:

T=Toe^u(x/sina)

calculate the V belt semi angle (a) given that:
The tension in the loaded part of the belt, T is 302 Newtons

The tension in the unloaded part of the belt To is 0.43 T

The coefficient of friction u is 0.3

The angle of lap is 148 deg

302=0.43ln^0.3(148/sina)

Where did this "ln" come from? Your original equation had an exponential.
Also is "x" really an angle? How do you know if it is to be measured in degrees rather than radians?

\(\displaystyle 302/0.43=ln^0.3(148/sina)

ln(302/0.43)=0.3(148/sina)

0.3(ln)(302/0.43)=148/sina

148(0.3)(ln)(302/0.43)=sina

sina =291.0152307

im stuck if this is not right and would love some help if i need it thanks\)

\(\displaystyle [/SUP]\)

 

[Ishuda]

Almost right and the confusion in the equations (log ln instead of exponential e) didn't help. Assume the values you gave are correct and the equation is correct. Let's start where you have it (almost) right
ln(T/To) = 0.3 * 148 / sin(a)
First let's just rearrange this as
sin(a) = 0.3 * 148 / ln(T/To) = 44.4 / ln(T/To)
Now, you were told that To = 0.43 T, NOT that T=302 and To=0.43 so the proper equation is
sin(a) = 44.4 / ln(T/To)
or, since ln(T/(0.43T)) = ln(1/0.43) = - ln(0.43) = 0.84387
sin(a) = 52.6085

Something is wrong; for this type of equation, sin(a) should be less than or equal to one is absolute value. If x were to be radians instead of degrees as suggested by HallsofIvy, then you would have
sin(a) = 0.918192...
which would at least be within the realm of possibility.

 

[getinthere]

Hi halls of ivy,
i thought ln was natural number e, also i thought thats where the angle would go.
if i am to be successful with this what should i do. thanks for the input already.:-D

 

[HallsofIvy]

Hi halls of ivy,
i thought ln was natural number e, also i thought thats where the angle would go.
if i am to be successful with this what should i do. thanks for the input already.:-D

Well, first, "ln" is a function while "e" is a number so, no, they are not the same. In fact, the function, ln(x), is the inverse of the function e^x. If you were not clear on that you need help from you teacher.

 

[getinthere]

Ok thanks for clearing that up halls of ivy, yeah i think you might be right its not a maths course im doing its HNC Electronics im good with theory side just lacking maths trying though teacher goes through it too fast then moves on to next bit im not sure what to do as we only do 1 half hours a week on the maths