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(II) At what minimumspeed must a rollercoaster be travelingwhen upside down atthe top of a circle(Fig. 42$)$ so that thepassengers do that fallout? Assume a radiusof curvature of 7.6 $\mathrm{m} .$

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$v=8.63 \mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 5

Using Newton's Laws: Friction, Circular Motion, Drag Forces

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Hope College

University of Winnipeg

McMaster University

Lectures

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

02:21

In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

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(II) At what minimumsp…

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(II) At what minimum speed…

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At what minimum speed must…

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What is the minimum speed …

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Determine the required hei…

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Consider a roller coaster …

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Roller coaster ride A roll…

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In Prob. $13.42,$ determin…

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In a loop-the-loop roller …

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Use the formula in Exercis…

So let's try the free body diagram of the roller coaster when it's upside down. So this is when the roller coaster is that the top. So we have a few passengers here now, um, first So for let's draw the free body diagram off the system so we have mg or the weight of the system, which is acting downwards. And if we see, say that this is the center off, the circular park then empties, acting straight towards the center. Similarly, the normal force is acting towards the center as well. Now, if we consider Donald direction, it's positive. Why access then the force that's acting towards the center. It should be f off n plus mg, which is equal to M times. They were a being the centripetal acceleration and from definition we know that M is equal to and b squared over r where he's the tendon, sheer speed. And from here, if we solve for the normal force, this becomes M times. Uh, these squared over r minus C. Now this normal force can also be viewed as a contact for So this is the minimum force that's required toe required for the roller coaster Toby in contact with the circular part. Now if this contact forces zero, that means that's the From there, we can get the minimum velocity. So basically the velocity should be more than the value or when the conduct for zero and that will give us the minimum velocity. So basically, lets make the contact for zero. If we do so, it's all for the velocity we see that V is equal to square root off our times g. So if we use ah, the numbers, we see that gravity is 9.8 meters per second squared and radius is given us 7.6 meters, which gives us the minimum velocity as 8.6 meters per second. So that means we need we need the velocity just more than eight point 6,000,000 meters for second toe. Have the contacts contact force non zero on That will be sufficient to keep the roller coaster in contact with the circular. Thank you.

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