Calculating the Angle of a Suspended Mass

• HardestPart
In summary, a mass of 6.10 kg suspended from a 1.51 m long string is revolving in a horizontal circle at a tangential speed of 3.24 m/s. To calculate the angle between the string and the vertical, the equation l*g*cos^2a+v^2cosa-l*g=0 is used. However, there was a mistake in the first posting of the quadratic and the correct solutions are 0.706 and -1.415. The first solution is incorrect as it is greater than 90 degrees, which is unphysical. Thus, the correct answer is the second solution.
HardestPart

Homework Statement

A mass of 6.10 kg is suspended from a 1.51 m long string. It revolves in a horizontal circle as shown in the figure
The tangential speed of the mass is 3.24 m/s. Calculate the angle between the string and the vertical.

F=mv^2/R

The Attempt at a Solution

The F component at y is:
Tcosa-mg=0
Tcosa=mg
T=mg/cosa
The F component at x is:
Tsina=ma
Tsina=mv^2/R
R=lsina
mg*sina/cosa=mv^2/lsina
lmgsin^2a=cosamv^2
lgsin^2a=v^2cosa

sin^2a=1-cos^2a
after putting all the numbers i get a final equation which is
10.798cos^2+10.4976cosa-14.798
the solution of the equation was
1-0.78
2-1.753

ofcourse i take the first one
BUT!its not correct!
pleasew tell me where i was wrong

Last edited by a moderator:
Your method is correct, but you made a mistake solving the quadratic. I recommend that you solve it symbolically and put in the numbers at the very end.

I am doing my calculations over and over again but am getting the same answer !
I can't see where i was wrong!

HardestPart said:
... after putting all the numbers i get a final equation which is
10.798cos^2+10.4976cosa-14.798
...

I should be able to help you if you show the equation (in symbols) before you put in the numbers and then what numbers you put in all laid out.

the equation is:
l*g(1-cos^2a)=v^2cosa
l*g*cos^2a+v^2cosa-l*g=0
that is befor i put in the numbers
after:
1.51*9.8*cos^2a+3.24^2cosa-1.51*9.8=0
14.798cos^2a+10.4976cosa-14.798=0
that is the final equation

did i make any mistake here?

HardestPart said:
the equation is:
l*g(1-cos^2a)=v^2cosa
l*g*cos^2a+v^2cosa-l*g=0
that is befor i put in the numbers
after:
1.51*9.8*cos^2a+3.24^2cosa-1.51*9.8=0
14.798cos^2a+10.4976cosa-14.798=0
that is the final equation

did i make any mistake here?

HardestPart said:
after putting all the numbers i get a final equation which is
10.798cos^2+10.4976cosa-14.798

I solved the equation with the correct one:
1-0.706
2--1.415

the first one is incorrect
could it be the second one?can it be negative?

HardestPart said:
I solved the equation with the correct one:
1-0.706
2--1.415

the first one is incorrect

How do you know it is incorrect? What is the correct answer?

[/quote]could it be the second one?can it be negative?[/QUOTE]

Don't forget you are solving for the cosine of an angle which cannot be less that -1. Also, a negative cosine means that the angle is greater than 90o which is unphysical.

I know its incorrect-thats complicated-
but I don't know what is the correct answer

Do you mean after i get my answers for the equation
I have to do SHIF COS A ->the solution i get
and than i get my angle?

HardestPart said:
I know its incorrect-thats complicated-
but I don't know what is the correct answer

Do you mean after i get my answers for the equation
I have to do SHIF COS A ->the solution i get
and than i get my angel?

I don't know about SHIF COS A, but the 0.706 that you found is the cosine of the angle. You need to find the angle itself from it and be sure you have the degrees/radians switches set properly.

1. How do you calculate the angle of a suspended mass?

To calculate the angle of a suspended mass, you will need to use trigonometric functions such as sine, cosine, and tangent. The angle can be found by taking the inverse of the trigonometric function of the ratio between the vertical and horizontal sides of the triangle formed by the suspended mass.

2. What is the purpose of calculating the angle of a suspended mass?

The calculation of the angle of a suspended mass is important in many fields such as engineering, physics, and mechanics. It helps to determine the forces acting on the mass and can be used to analyze the stability and dynamics of the system.

3. What factors can affect the accuracy of the angle calculation?

The accuracy of the angle calculation can be affected by factors such as the precision of the measurements, the stability of the suspension system, and the presence of external forces or disturbances. It is important to minimize these factors to obtain a more accurate angle measurement.

4. Can the angle of a suspended mass change over time?

Yes, the angle of a suspended mass can change over time due to various factors such as the movement of the mass, changes in the suspension system, and the effects of external forces. It is important to continuously monitor and adjust the angle calculation to account for these changes.

5. Are there any alternative methods for calculating the angle of a suspended mass?

Yes, there are alternative methods for calculating the angle of a suspended mass such as using a protractor or using a digital inclinometer. These methods may be more suitable for certain situations, but the basic principles of trigonometry still apply in the calculation of the angle.

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