What is the angle between the string and the vertical?

In summary, the problem involves a mass of 3.900 kg suspended from a 1.450 m long string and revolving in a horizontal circle. The tangential speed of the mass is 3.247 m/s. To calculate the angle between the string and the vertical, one must consider the forces acting on the mass and use the equation sin(theta) = v^2/gsin(theta)L to solve for the angle.
  • #1
BrimmZERO
2
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"A mass of 3.900 kg is suspended from a 1.450 m long string. It revolves in a horizontal circle.
The tangential speed of the mass is 3.247 m/s. Calculate the angle between the string and the vertical (in degrees)."

Here is a diagram, labelling angle theta I'm supposed to solve for: http://capaserv.physics.mun.ca/msuphysicslib/Graphics/Gtype11/prob03_pendulum.gif

I've deduced so far that: sin(theta) = opp/hyp

In this case, opp = radius and hyp = length of string (L) or (1.450 m)

So sin(theta) = r/L

In turn, r can be solved by means of Fc = mv^2/r, as r = mv^2/Fc

so sin(theta) = mv^2/FcL

M is given, V is given, and L is given. Fc I'm sort of puzzled on, since I can't use the MV^2/R equation again. Any clues?
 
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  • #2
Hint: What provides the centripetal force?
Hint: Consider both vertical and horizontal forces acting on the mass.
 
  • #3
Okay, I think I'm getting somewhere. Would it be right to say the Fc is equal to the x-factor of the weight of the mass on the string? I could say this therefore:

Fc = mgsin(theta)

and then

sin(theta) = mv^2/mgsin(theta)L

which would cancel mass, giving me:

sin(theta) = v^2/gsin(theta)L

would that be right? or is mass even significant in this problem?
 
  • #4
Not right. For one thing, the weight of the mass acts down--it has no horizontal component.

Try this: Identify all the forces acting on the mass. (There are two forces.) Then consider horizontal and vertical components.
 

FAQ: What is the angle between the string and the vertical?

1. What is centripetal motion?

Centripetal motion is the movement of an object in a circular path around a fixed point. It is caused by a centripetal force, which is directed towards the center of the circle and keeps the object moving in a curved path.

2. How is centripetal force calculated?

The centripetal force can be calculated using the formula F = mv^2/r, where F is the force, m is the mass of the object, v is the velocity, and r is the radius of the circle. This formula is derived from Newton's second law of motion, which states that force is equal to mass times acceleration.

3. What are some examples of centripetal motion?

There are many examples of centripetal motion, such as a car turning a corner, a satellite orbiting the Earth, or a merry-go-round spinning. Anytime an object is moving in a circular path, it is experiencing centripetal motion.

4. How does centripetal force affect the speed of an object?

Centripetal force does not directly affect the speed of an object. It only causes a change in the direction of the object's velocity, keeping it moving in a curved path. However, if the centripetal force is removed, the object will move in a straight line at a constant speed, due to Newton's first law of motion.

5. How does centripetal motion differ from centrifugal motion?

Centripetal motion is the inward force that keeps an object moving in a circular path, while centrifugal motion is the outward force that is experienced in a rotating frame of reference. Centrifugal force is often described as a "fictitious force," as it is not a real force but rather an apparent force experienced by an observer in a rotating frame of reference.

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