# Need help finding force components.

• kambrian
In summary: And the second part is when it is on the circular loop, and I need to find the radius and the gravitational force?
kambrian
I am having a problem with this question. I can't figure out how to approach it.

A solid sphere of mass m and radius r rolls without slipping along the track. it starts from rest with the lowest point of the sphere at height h above the bottom of the loop of radius R, much larger than r.

What are the force components on the sphere at he point P if h = 3R?

How would I go about solving this problem? I attached a picture of the situation.

#### Attachments

• problem.JPG
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Well you need to split up this problem. First, the sphere moves down the incline under the influence of gravity (thus, there will also be a normal force)

Then, secondly, it moves along a loop, which is circular. Then, there must be some centripetal force and also gravity right ?

regards
marlon

You know, just to elaborate, there is a great classic associated with this figure. Suppose we let a point particle of mass m (the solution is analoguous for a solid object, you only will need to incorporate the rotational inertia I) slide down the incline from heigth h. What will this h be as a function of radius r, in the case that the object must STOP at the top of the loop.

Well, first we study the motion along the incline : energy conservation learns us :

mgh =1/2mv² and thus v² = 2gh

Then, we study the loop : there will be both gravity and centripetal force (mv²/r) on the object. At the top : mv²/r = mg (the centripetal force must eliminate gravity. Well, actually this is the centrifugal force, directed along the opposite direction of the centripetal force) : mg = (mv²)/r and thus v² = gr

Again applying energy conservation between bottom and top of the loop learns us :

1/2mv² (here v² = 2gh) = mg2r + 1/2mv² (here v² = gr)

This eaquation gives : mgh = mg2r + mgr/2 --> h = 2r + r/2 = 5r/2

regards
marlon

Im still not seeing how I would do this. You said to split it up into two parts but what exactly am I trying to find in these two separate parts?

I am assuming the first part, when the ball is rolling down the incline, I am trying to find the velocity, right?

## 1. What are force components?

Force components refer to the individual forces that make up a larger force vector. They are typically represented as horizontal and vertical forces, and can be calculated using trigonometry.

## 2. How do I find force components?

To find force components, you will need to know the magnitude and direction of the force vector. You can then use trigonometric functions, such as sine and cosine, to calculate the horizontal and vertical components of the force.

## 3. Why is it important to find force components?

Finding force components allows you to better understand the forces acting on an object and how they may affect its motion. It also allows for more accurate calculations and predictions in physics and engineering.

## 4. Can force components be negative?

Yes, force components can be negative. This occurs when the force vector is acting in the opposite direction of the chosen coordinate system. It is important to pay attention to the signs of the components when calculating and interpreting them.

## 5. Are there any other methods for finding force components?

Yes, there are other methods for finding force components such as using the Pythagorean theorem and inverse trigonometric functions. However, using trigonometry is the most common and efficient method for finding force components.

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