# Help Needed: Solving a Block Sliding Down an Inclined Plane into a Loop-the-Loop

• n_ds
In summary: So at the top of the loop, mg=m\frac{v^2}{r} and the force acting on the object is mg\frac{v^2}{r}=mgh.
n_ds
Hi

I am working on an assignment and I honeslty am completely baffled with this question. I have no idea how to go about trying to figure it out as its purely conceptual based. If anyone has any info that might help, I am all ears. The problem is as follows and I am attaching the diagram as well if it helps:

A block of mass m slides down an inclined plane into a loop-the-loop of radius r . (a) Neglecting friction, what is the minimum speed the block must have at the highest point of the loop in order to stay in the loop? [Hint: What force must act on the block at the top of the loop to keep the block on a circular path?] (b) At what vertical height on the inclined plane (in terms of the radius of the loop) must the block be released if it is to have the required minimum speed at the top of the loop?

Thanks

TN

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• physics problem.JPG
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If you had used the homework posting template (please get in the habit of doing that), one of the sections asks what equations and/or priciples apply to your question. What can you tell us about that?

I did not post any formulas because I am not sure what I can use. Like this question doesent use any numbers, you are only supplied with generalizations of certain aspects. Like friction is negligaable. Also since the cart is at a height you can use potential energy formula. But I still can't find a formula that i could use to solve for speed. I know it has to do with centrifugal force but I am just not sure. That is why i am asking.

Well at least you're starting to use some of the right keywords. Show us some equations for the KE and PE of an object, and tell us about the total energe TE. What equations govern circular motion? What equation would you use to figure out the forces on an object that is exhibiting uniform circular motion?

Remember that at the top of the loop $$mg=m\frac{v^2}{r}$$

## 1. How do you calculate the velocity of the block as it slides down the inclined plane?

The velocity of the block can be calculated using the formula v = √(2gh), where v is the velocity, g is the acceleration due to gravity, and h is the height of the inclined plane.

## 2. What factors affect the block's ability to successfully complete the loop-the-loop?

The factors that affect the block's ability to successfully complete the loop-the-loop include the velocity of the block, the angle and height of the inclined plane, and the radius of the loop-the-loop.

## 3. How do you determine the minimum velocity needed for the block to complete the loop-the-loop?

The minimum velocity needed for the block to complete the loop-the-loop can be calculated using the formula v = √(rg), where v is the velocity, r is the radius of the loop-the-loop, and g is the acceleration due to gravity. This is known as the minimum centripetal velocity.

## 4. How does the mass of the block affect its motion down the inclined plane and through the loop-the-loop?

The mass of the block does not significantly affect its motion down the inclined plane, as long as gravitational force is greater than the force of friction. However, a heavier block may require a higher minimum velocity to successfully complete the loop-the-loop due to the increased force of gravity.

## 5. What safety precautions should be taken when conducting an experiment with a block sliding down an inclined plane into a loop-the-loop?

When conducting experiments, it is important to follow proper safety precautions such as wearing protective gear, securing the inclined plane and loop-the-loop to a stable surface, and using a barrier to prevent the block from flying off the track. It is also important to use appropriate materials and conduct the experiment in a controlled environment.

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