Why is mg=mv^2/r for centripetal motion instead of mg+T=mv^2/r?

In summary, the equation mg=mv^2/r is used for centripetal motion because it takes into account the gravitational force and the centripetal force, which is provided by the tension in the string or rope that is keeping the object in circular motion. This equation allows for a more accurate calculation of the centripetal force, as it considers both the mass and velocity of the object, as well as the radius of the circular path. On the other hand, the equation mg+T=mv^2/r only takes into account the gravitational force and the tension force, but does not consider the mass or velocity of the object. This can lead to less precise calculations and does not fully account for all the forces at play in cent
  • #1
jack1234
133
0
Hi, for this question
http://tinyurl.com/2qgco5
this is the solution for (b)
http://tinyurl.com/yrl64q

May I know why for centripetal motion, it is mg=mv^2/r, but not mg+T=mv^2/r (T is the tension of the rope)?
 
Last edited:
Physics news on Phys.org
  • #2
Because the rope is acting perpendicular to the motion and is prescisely enough to offset the force of gravity in that direction.
 
  • #3
Sorry, I am not very clear for the explanation.
I assume "the rope is acting perpendicular to the motion" is the downward force for the tension of rope, visually, it is two forces acting on the object, one is the tension of rope, one is the gravitational force, I am not sure what is the incorrectness of my thinking...
 
  • #4
jack1234 said:
Sorry, I am not very clear for the explanation.
I assume "the rope is acting perpendicular to the motion" is the downward force for the tension of rope, visually, it is two forces acting on the object, one is the tension of rope, one is the gravitational force, I am not sure what is the incorrectness of my thinking...
Don't forget that you are looking for just enough energy to have the pendulum complete a full circle around the peg...in which case there is no tension at the top of its circle, and the only force acting on the pendulum is gravity at that particular point.
 

FAQ: Why is mg=mv^2/r for centripetal motion instead of mg+T=mv^2/r?

What is tension of rope?

Tension of rope refers to the pulling force applied to a rope or cable. It is the measure of how much force is exerted on the rope in order to keep it taut.

How is tension of rope calculated?

Tension of rope is calculated using the formula T = F * L, where T is the tension, F is the force applied, and L is the length of the rope.

Why is tension of rope important?

Tension of rope is important because it affects the stability and strength of structures that use ropes, such as bridges and cranes. It also plays a crucial role in determining the maximum weight that can be lifted using a rope.

How does the material of the rope affect its tension?

The material of the rope can affect its tension in a few ways. For example, a rope made of a stronger material can withstand a higher tension before breaking. On the other hand, a more elastic material may stretch more under the same tension, which can affect its overall strength and stability.

What factors can change the tension of a rope?

The tension of a rope can be affected by a number of factors, including the weight of the load being lifted, the angle at which the rope is being pulled, and the condition of the rope itself (such as fraying or wear and tear). Temperature and humidity can also impact the tension of a rope, as they can cause the material to expand or contract.

Similar threads

Loop the Loop Problem Solution | N > 0, Energy Conservation Method
Replies
8
Views
2K
Need help explaining this Centripetal force problem
Replies
5
Views
2K
Is it friction or tension acting on the person hanging on a rope?
Replies
4
Views
482
Tension and Centripetal Force in Circular Motion
Replies
2
Views
2K
Determine the speed and tension of keys swinging in a circular path
Replies
8
Views
1K
Tension in a rope hanging between 2 trees
Replies
24
Views
672
Circular Motion of a Cyclist and a Car going around a bend in the road
Replies
6
Views
3K
Finding the period of the satellite's orbital motion
Replies
1
Views
1K
Vertical circle in a pendulum ride -- tension force acting on the gondola
Replies
7
Views
2K
Finding the distance of a peg so that a pendulum can circle around it
Replies
2
Views
319

Hot Threads

Recent Insights

Back
Top