Thread: Tension & Rads

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.

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.

Rewrite your equation:




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

-Dan

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.

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.

Do the linear regression. That means you are modeling the data for ln(T) and as a line. The computer/calculator will give you a value for the slope and the y - intercept. The slope will be and the intercept will be . So .

-Dan