# Loop the Loop and block

In summary, the minimum height for a block to start from rest and still make it around a frictionless loop the loop track is 2.5 times the radius of the loop. This can be found by applying conservation of energy and Newton's 2nd law to determine the minimum speed required for the block to stay on the track.

[SOLVED] Loop the Loop

1. Homework Statement

A block slides on the frictionless loop the lopp track shown in this img, what is the min height at which it can start from rest and still make it around the loop

## The Attempt at a Solution

I haev solved this problem TWO ways, and i can't decide which way is correct

the eqn...

U0+K0 = K+U

where U = potential energy and K = kinetic energy

first

m * g * h + (1/2) * m * v^2 >= m * g * 2 * R

final answer = h = 2R

the way my friend set it up and solved it

m * g * h >= (1/2) * m * v^2 + m * g * 2 * R

my friend solved it this way and got h = (5*R) / 2

but i can't seem to get what he got and i get h=h-2r+2r which says the min height has to be the min height of the radius aka h = 2R

For one thing, the initial energy is completely potential since it starts from rest (KE = 0). So the first method doesn't make sense.

The trick is to figure out what KE the block must have at the top of the loop in order to maintain contact with the track.

m * g * h >= (1/2) * m * v^2 + m * g * 2 * R

you can solve for v^2 and get

v^2 = 2g(h-2R)

that would be what is required to stay on the track, so would u plug that back into

m * g * h >= (1/2) * m * v^2 + m * g * 2 * R

m * g * h >= (1/2) * m * (2g(h-2R)) + m * g * 2 * R

cancel mass, g cancels, .5 *2 =1

g*h >= (1/2)*(2g(h-2R)) + g*2*R

g*h >= g(h-2R)) + g*2*R

h >= h-2R + 2*R

would this be the correct eqn to solve for min height?

Last edited:

m * g * h >= (1/2) * m * v^2 + m * g * 2 * R
This is conservation of energy. It's necessary but not sufficient to solve this problem. Hint: Apply Newton's 2nd law.

i guess you're still not understanding what's the condition to the block doesn't feel down from the loop...

what the block has in top of the look to don't fell down? first you need to understand that...

mg = (mv^2) /R

you can find min speed so it doesn't fall off the track this way

R*g = v^2

Last edited:

m * g * h >= (1/2) * m * v^2 + m * g * 2 * R
m * g * h >= (1/2) * m * R*g + m * g * 2 * R

h >=1/2 R + 2 R

h >= 2.5 R

Good!

thanks! i totally looked at that v^2 the wrong way

## 1. What is a "Loop the Loop and block" in science?

A "Loop the Loop and block" is a common term used in scientific experiments and research to describe a process of continuously repeating a series of actions or steps, while also adding a barrier or obstacle in the loop to observe its effects.

## 2. How is "Loop the Loop and block" used in scientific experiments?

Scientists use "Loop the Loop and block" in experiments to understand cause and effect relationships. By repeating a series of actions and adding a block, they can observe how the block affects the outcome of the loop and draw conclusions about the relationship between the two variables.

## 3. What are some examples of "Loop the Loop and block" in science?

One example of "Loop the Loop and block" in science is the classic Pavlov's dog experiment, where a bell (loop) is repeatedly rung before giving a dog food (block), leading to the dog salivating at the sound of the bell alone. Another example is adding a barrier in a maze to study the learning and problem-solving abilities of rats.

## 4. What are the benefits of using "Loop the Loop and block" in scientific research?

Using "Loop the Loop and block" in scientific research allows for controlled experiments and the ability to isolate and study the effects of specific variables. It also allows for the repetition of results, leading to more reliable and conclusive findings.

## 5. What are some limitations of using "Loop the Loop and block" in scientific experiments?

One limitation of using "Loop the Loop and block" in scientific experiments is that it may not accurately reflect real-world situations and may oversimplify complex phenomena. It also requires careful design and control to avoid confounding variables that may affect the results.