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A motorcycle is traveling up one side of a hill and down the other side. The crest of the hill is a circular arc with a radius of 45.0 m. Determine the maximum speed that the cycle can have while moving over the crest without losing contact with the road.

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$\mathrm{v}=21.0 \mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 5

Dynamics of Uniform Circular Motion

Newton's Laws of Motion

Applying Newton's Laws

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Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

03:43

In physics, dynamics is the branch of physics concerned with the study of forces and their effect on matter, commonly in the context of motion. In everyday usage, "dynamics" usually refers to a set of laws that describe the motion of bodies under the action of a system of forces. The motion of a body is described by its position and its velocity as the time value varies. The science of dynamics can be subdivided into, Dynamics of a rigid body, which deals with the motion of a rigid body in the frame of reference where it is considered to be a rigid body. Dynamics of a continuum, which deals with the motion of a continuous system, in the frame of reference where the system is considered to be a continuum.

01:40

A motorcycle is traveling …

03:49

A car approaches the top o…

03:25

A bicycle is rolling down …

03:08

When crossing an intersect…

04:59

A motorcycle has to move w…

02:43

A motorcycle has a constan…

02:30

in this problem, we have to find that the max of the maximum velocity that a biker can go over a hill with a given radius. So as we can see from our free body diagram, when the writers of the exact top of the hill we have the gravitational force 20 downward and the normal fourth pointing upward opposing it, you know the normal force is what's important to this problem. You might remember reading in your textbook that the maximum velocity that we can ever cross surface that was in contact is when the normal force is equal 20 any less than that and we fly off. Which makes sense since the normal force is what is opposing gravity. If the number of poor sport starts pointing office in the opposite direction, being negative, then we start flying off whatever service went on. So if we try to find the very maximum velocity, we set the double force equal to zero, and that means that we only have one force in the problem. Now. MG, an MG is what's pointing towards the centre of our circular motion so it must be equal to M B squared over R R centripetal force. We want to sulfur for V in this problem. So we're gonna cancel out our EMS and we find that V is equal to the square root of g times are nog is just 9.8 meters per second, squared the acceleration of gravity and are because we're given in the problem is 45 meters. We do that out. We find that our maximum V is equal to 21.0 meters per second. And that's all we have to do to solve this problem. Just remember that they went everything normal forces zero. That's the maximum.

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