Uniform Circular Motion: A plum-bob makes a 70 degree angle...

In summary, the concept of uniform circular motion is illustrated through the behavior of a plum-bob making a 70-degree angle with the vertical. This setup demonstrates how the tension in the string and the gravitational force interact to maintain circular motion, highlighting the balance of forces acting on the bob. The angle indicates the relationship between the forces involved, emphasizing the principles of circular motion and the effects of gravity on the system.
  • #1
daisy7777
16
1
Homework Statement
You are spin a merry-go-round and are trying to use a hanging plum bob attached to the outermost limb of the merry-go-round to measure the period of the merry-go-round. If the plum bob is 20.0 cm long, has a mass of 50.0 g on it, the merry-go-round has a radius of 1.25 m and you observe the plum bob make a 70.0 degree angle with the vertical on the outermost edge of the merry-go-round, what is the period of the merry-go-round?

I attached an image of what I've tried. I don't think this is right though. Shouldn't the centripetal force be equal to the acceleration of the bob * the mass of it?
Relevant Equations
Fc = ma
Fc = (4pi^2rm)/T
unnamed (1).jpg

I also tried to solve for T when the centripetal force is equal to the tension in the x-dir, but I got 2.174s and that's not the right answer either. I'm not sure what I'm doing wrong exactly.
 
Physics news on Phys.org
  • #2
What is your sum of the forces in the ##x## direction( radial)? We strongly prefer that you use latex to present your mathematics of hand written notes. Please see the latex guide.
 
  • Like
Likes SammyS
  • #3
daisy7777 said:
Homework Statement: You are spin a merry-go-round and are trying to use a hanging plum bob attached to the outermost limb of the merry-go-round to measure the period of the merry-go-round. If the plum bob is 20.0 cm long, has a mass of 50.0 g on it, the merry-go-round has a radius of 1.25 m and you observe the plum bob make a 70.0 degree angle with the vertical on the outermost edge of the merry-go-round, what is the period of the merry-go-round?

I attached an image of what I've tried. I don't think this is right though. Shouldn't the centripetal force be equal to the acceleration of the bob * the mass of it?
Relevant Equations: Fc = ma
Fc = (4pi^2rm)/T

View attachment 341841
I also tried to solve for T when the centripetal force is equal to the tension in the x-dir, but I got 2.174s and that's not the right answer either. I'm not sure what I'm doing wrong exactly.
I would resist the temptation to put in the numbers at the earliest opportunity. Note that the mass of the bob is irrelevant. I would pick things up from:
$$a_c = g\tan x$$Can you find a relationship between ##a_c## and ##T##?

PS personally, I would use ##\theta## as the angle. Especially in a mechanics problem.
 
  • Like
Likes SammyS
  • #4
daisy7777 said:
If the plum bob is 20.0 cm long,.., the merry-go-round has a radius of 1.25 m and you observe the plum bob make a 70.0 degree angle with the vertical on the outermost edge of the merry-go-round
From the wording in the question, I'd say that the radius of motion (of the bob) is bigger than 1.25m. The upper end of the pendulum is 1.25m from the centre, but the bob itself is further out. You've ignored that - and that's probably the mistake.

Your calculation seems correct apart from the point noted above. But there are some points to note:
- your top drawing shows tension acting vertically upwards; it doesn't!
- you have created unecessary work (and risk of errors) by using values rather than symbols in the inermediate steps (as already noted by @PeroK);
- you have equations which illegally mix scalars and vectors (e.g. you shouldn't equate a scalar to a vector).

Edit: Minor rewording only.
 
Last edited:
  • Like
Likes erobz and PeroK
  • #5
daisy7777 said:
I also tried to solve for T when the centripetal force is equal to the tension in the x-dir, but I got 2.174s
I don't see how that is different from the attempt you posted (assuming you again did not allow for the horizontal component of the string length, as @Steve4Physics points out), so you should have got the same answer.

Btw, it's "plumb bob", from the Latin plumbum=lead (the metal) as in plumber.
 
Last edited:

FAQ: Uniform Circular Motion: A plum-bob makes a 70 degree angle...

What is uniform circular motion?

Uniform circular motion refers to the motion of an object traveling at a constant speed along a circular path. Despite the constant speed, the direction of the object's velocity changes continuously, which means the object is always accelerating towards the center of the circle.

How does the angle of the plum-bob relate to uniform circular motion?

The angle of the plum-bob, in this case, 70 degrees, indicates the tilt caused by the centripetal force acting on the bob as it moves in a circular path. This angle helps in analyzing the forces acting on the bob, including tension in the string and gravitational force, to understand the dynamics of its circular motion.

What forces are acting on the plum-bob in uniform circular motion?

In uniform circular motion, the forces acting on the plum-bob include the gravitational force pulling it downward, the tension in the string providing the centripetal force needed for circular motion, and the component of tension that balances the gravitational force. The resultant of these forces ensures the bob moves in a circular path at a constant speed.

How do you calculate the centripetal force in this scenario?

The centripetal force can be calculated using the formula \( F_c = m \cdot v^2 / r \), where \( m \) is the mass of the plum-bob, \( v \) is its tangential speed, and \( r \) is the radius of the circular path. The radius can be determined from the length of the string and the angle it makes with the vertical.

What role does the 70-degree angle play in determining the radius of the circular path?

The 70-degree angle helps in determining the horizontal and vertical components of the forces acting on the plum-bob. By using trigonometric relationships, the length of the string, and the angle, you can calculate the radius of the circular path. Specifically, \( r = L \cdot \sin(\theta) \), where \( L \) is the length of the string and \( \theta \) is the angle with the vertical.

Similar threads

Acceleration in uniform circular motion is uniform or non-uniform?
2
Replies
55
Views
2K
A Car on a Banked Curve Moving in Uniform Circular Motion
Replies
7
Views
2K
Uniform Circular Motion: Tension Force at Top of Circle
Replies
4
Views
647
Is Vertical Circular Motion Ever Uniform?
Replies
10
Views
2K
Deviation of Plumb Bob In Uniform Circular Motion
Replies
11
Views
2K
Circular Motion Questions (energies, forces, angular velocities, etc.)
Replies
2
Views
1K
Circular Motion of a Cyclist and a Car going around a bend in the road
Replies
6
Views
3K
Acceleration in non-uniform circular motion
Replies
1
Views
1K
Circular Motion: Tension in String w/ Bob Weight
Replies
8
Views
1K
Circular motion of a rotational spring
Replies
12
Views
3K

Hot Threads

Recent Insights

Back
Top