Hi, I've got a question that I can't see how to do it, it is:

The tension T in a belt passing round a pulley wheel and in contact with the pulley over an angle of θ radians is given by T=Toe^μθ
Where To and μ are constant. Experimental results obtained are:

T Newtons: 47.9 52.8 60.3 70.1 80.9

θ radians : 1.12 1.48 1.97 2.53 3.06

Determine approximate values of To and μ. Hence find the tension when θ is 2.25 radians and the value of θ when the tension is 50 Newtons.

Any help would be greatly appreciated,

Thanks.

2. Originally Posted by gram1210
Hi, I've got a question that I can't see how to do it, it is:

The tension T in a belt passing round a pulley wheel and in contact with the pulley over an angle of θ radians is given by T=Toe^μθ
Where To and μ are constant. Experimental results obtained are:

T Newtons: 47.9 52.8 60.3 70.1 80.9

θ radians : 1.12 1.48 1.97 2.53 3.06

Determine approximate values of To and μ. Hence find the tension when θ is 2.25 radians and the value of θ when the tension is 50 Newtons.

Any help would be greatly appreciated,

Thanks.
$\displaystyle T = T_0 e^{\mu \theta}$

$\displaystyle ln(T) = \mu \theta + ln(T_0)$

If you plot your data as ln(T) vs. $\displaystyle \theta$ (y vs. x) then your data should form a line with slope $\displaystyle \mu$ and intercept $\displaystyle ln(T_0)$. So calculate ln(T) for your data set and do a linear regression on ln(T) vs. $\displaystyle \theta$.

-Dan

3. So, as μ and To are constants, how do I calculate their values?

That then links into the graph..where does the interception between μ and ln(To) come into existance?

Thanks again.

4. Originally Posted by gram1210
So, as μ and To are constants, how do I calculate their values?

That then links into the graph..where does the interception between μ and ln(To) come into existance?

Thanks again.
$\displaystyle ln(T) = \mu \theta + ln(T_0)$

Do the linear regression. That means you are modeling the data for ln(T) and $\displaystyle \theta$ as a line. The computer/calculator will give you a value for the slope and the y - intercept. The slope will be $\displaystyle \mu$ and the intercept will be $\displaystyle ln(T_0)$. So $\displaystyle T_0 = e^{\text{intercept}}$.

-Dan