Solve Conical Pendulum: Find Speed, Period, Horiz. Comp., Rad. Accel.

In summary, the conical pendulum is a small object of mass m suspended from a string of length L = 1.8 m, revolving in a horizontal circle of radius r with constant speed v and angle = 28°. The speed of the object is found to be 2.098, and the period of revolution is 2.53. For a conical pendulum with m = 14.0 kg, the horizontal and vertical components exerted by the string on the object can be found using the equation T=ma/sin theta, where T is the tension in the string and theta is the angle of the string with the horizontal. The radial acceleration of the object can be calculated using the equation a=s/t
  • #1
coolskool
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The Conical Pendulum


A small object of mass m is suspended from a string of length L = 1.8 m. The object revolves in a horizontal circle of radius r with constant speed v and angle = 28°

Find the speed of the object.
i found s=v=2.098.

Find the period of revolution, defined as the time interval required to complete one revolution.
i found it to be ... t=2.53

NOW...

For the conical pendulum described above, determine the following if m = 14.0 kg.
(a) the horizontal and vertical components exerted by the string on the object
(b) the radial acceleration of the object.

for H my equation is
T=ma/sin theta

and to find a=s/t
i take what i found in the previous problem right?
so s=v=2.098
and t=2.53?

and for Fv my equation is T=mg/costheta?

and then for part b...mv^2/r...
but what is r?

OKAY i found everything BUT the HORIZONTAL COMPONENT!
HELP
 
Last edited:
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  • #2
For the first part I get a slightly different answer for the speed and period. your answers are round about the same as mine so perhaps just using different constants.

For parts a and b, you will have to go back to the circular motion equations and find the horizontal force being exerted on the bob.

part b the equation you have used is for force but you want acceleration. Remember F=ma. Also you should know what r is from the first part of the question. Its simply a matter of trigonometry (i.e. the pendulum string forms a right angled triangle with the vertical and horizontal and you know the hypotenuse and one of the angles).
 
  • #3


I would first commend you on your efforts in solving the conical pendulum problem and finding the speed and period of revolution. However, it seems like you may have some confusion with the equations and concepts involved in this problem.

To find the horizontal component of the force exerted by the string on the object, we can use the equation you mentioned, T=ma/sinθ. However, the equation you provided for finding the radial acceleration, a=s/t, is incorrect. The correct equation is a=v^2/r, where v is the speed and r is the radius of the circle. In this case, the radius is not given, but it can be calculated using the angle and the length of the string. Since the angle is given in degrees, it would be helpful to convert it to radians first (θ = 28° * π/180 = 0.488 radians). Then, the radius can be calculated as r = L * sinθ = 1.8 * sin(0.488) = 0.906 m.

So, to find the horizontal component of the force, we can plug in the values we have into the equation: T=ma/sinθ. The mass is given as 14.0 kg and the angle is 0.488 radians. We can also use the value we found for the period, t=2.53, instead of the speed since we know that t = 2πr/v. So, the equation becomes:

T = ma/sinθ
t = 2πr/v
2.53 = 2π(0.906)/v
v = 2π(0.906)/2.53 = 2.261 m/s

Now, we can plug in all the values into the equation for the horizontal component of the force:

T=ma/sinθ
T=(14.0)(2.261)/sin(0.488)
T= 31.7 N

Therefore, the horizontal component of the force exerted by the string on the object is 31.7 N.

For the vertical component, we can use the equation you mentioned, T=mg/cosθ. Again, we can use the value we found for the period, t=2.53, instead of the speed. So, the equation becomes:

T=mg/cosθ
T=(14.0)(9.8)/cos
 

1. How do you find the speed of a conical pendulum?

To find the speed of a conical pendulum, you can use the equation v = √(gRtanθ), where g is the acceleration due to gravity, R is the length of the pendulum's rope, and θ is the angle between the rope and the vertical axis.

2. What is the period of a conical pendulum?

The period of a conical pendulum is the time it takes for one complete revolution. It can be calculated using the equation T = 2π√(R/g), where R is the length of the pendulum's rope and g is the acceleration due to gravity.

3. How do you calculate the horizontal component of a conical pendulum's motion?

The horizontal component of a conical pendulum's motion can be calculated using the equation aH = v²/R, where v is the speed of the pendulum and R is the length of its rope.

4. What is the radial acceleration of a conical pendulum?

The radial acceleration of a conical pendulum is the acceleration towards the center of the circle it is swinging in. It can be calculated using the equation aR = v²/R, where v is the speed of the pendulum and R is the length of its rope.

5. How does the angle of the rope affect the motion of a conical pendulum?

The angle of the rope affects the motion of a conical pendulum by changing the speed, period, and radial acceleration of the pendulum. A larger angle will result in a faster speed, shorter period, and larger radial acceleration, while a smaller angle will result in a slower speed, longer period, and smaller radial acceleration.

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