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Show that on a roller coaster with a circular vertical loop (Fig, 43), the difference in your apparent weight at the top of the loop and the bottom of the loop is $6 g^{\prime} s-$ that is six times your weight. Ignore friction. Show also that as long as your speed is above theminimum needed, this answer doesn't depend on the size of the loop orhow fast you go through it.

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$6 m g$

Physics 101 Mechanics

Chapter 8

Conservation of Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Wilson K.

December 19, 2020

how to find the difference between vb2 and vt2

Cornell University

University of Washington

Hope College

McMaster University

Lectures

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

05:23

Show that on a roller coas…

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10:16

03:03

Suppose you are riding on …

01:29

You are riding a roller co…

03:53

Modern roller coasters use…

04:24

Loop-the-loop You ride a r…

13:04

If the track is to be desi…

04:33

Part of a roller-coaster r…

02:42

You ride a roller coaster …

01:30

Consider the roller coaste…

01:33

The track near the top of …

03:06

Modern roller coasters ha…

03:27

What is the apparent weigh…

So for this roller coaster problem, we can draw a force diagram at the bottom of the loop. So where the bottom of the loop? The forced diagram. The two forces acting here We have the normal force and we have mg Victor at the bottom of the loop here, enjoy slightly bigger. So the net force are the boredom is F n border minus mg which is equals to the centripetal force which is M B bottom squared. Well, what are so that implies that f and bottom there's a normal force of the bottom is given by m g bless and the bottom squired by our So that is our the question of the bottom of the loop? No, at the top of the loop here at the top of the look. So we have that roller coaster in this condition. Here the forces are normal force at the top and we have the gravity vector force of gravity back turn, which is F g, which is equal to m g Sonett fours on the top. His equals to the normal force is on the top less mg because they're in the same direction and that should be equals two. The centripetal force, which is N v top squared by our, which implies that the normal force is on the top is equals to em. V tac squared over R minus mg. So we got the two equations for the normal force is on the bottom and on the top. Now we assumed that the door coaster When it goes on the top, it doesn't fall down, which means that the normal force in the top are greater than zero. So we can also say that Vito is better than RG basically. So now we'll apply the law of conservation of energy. The level of one represents the corset at the bottom of the loop. So this is the level one and this is level two at the top of the loop. And the level of the bottom of the loop is zero location. So the longer roller coaster, you know, is going from the bottom to the top here. And the level of the bottom is 00 locations of eyes equals to zero and our dislocation, the why which is the height gained is equals to two are so the total energy is conserved. These two locations. So what I don't even is equals to Mito, which implies that had these two locations have and even squared less mg by one should be equals do half M V two squared less N g Y two. So if you plug in the values in this equation, which implies that you will get we bottom squared is equals to be top squared plus four g r. So you can just looking in the value just like why one is equal to zero. We'll give I to hear. And this location here is to our and we are We can actually calculate the V one and me too at two locations and relationship will be This may be squared is equal beauty squared less for gr and what they're asking here is the difference in the apple and waits. So the difference in apple and waits the difference in the apple ingrates is actually difference of the normal forces because apple and weight is what you feel and you feel the normal force. So it is the F and B minus f and duck, so worth the difference in these two. So if you look at these two equations so you will get mg bless and the bottom squired by our and subtracting it too. Envy top squared by our minus energy. So I just go on to the next page for this. So if you rearrange this equation and saw that so you're beginning to m g bless em. The bottom squared minus V top squared. Well, what are so that should give you two mg? Bless em. And we know that the difference in the bottom and veto already equals 24 g r divided by our So that should give you a six mg. Now, as you can see that this result what you have got does not contain are there is no are here and that is no v here. So therefore, this answer does not depend, you know, on the size of the loop and also on how fast you go on Look

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