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A motorcycle has a constant speed of 25.0 m/s as it passes over the top of a hill whose radius of curvature is 126 m. The mass of the motorcycle and driver is 342 kg. Find the magnitudes of (a) the centripetal force and (b) the normal force that acts on the cycle.

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$1.70 \times 10^{3} N$$1.66 \times 10^{3} N$

Physics 101 Mechanics

Chapter 5

Dynamics of Uniform Circular Motion

Newton's Laws of Motion

Applying Newton's Laws

University of Michigan - Ann Arbor

University of Washington

Hope College

University of Sheffield

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.

02:31

A motorcycle has a constan…

02:43

01:15

A bicyclist travels in a c…

02:03

01:44

A $225-\mathrm{kg}$ dirt b…

01:42

- - A As part of a circus …

01:11

$\mathrm{A} 1400 \mathrm{k…

10:34

(III) A cyclist intends to…

02:22

A car of mass $1000 \mathr…

01:16

A toy car moving at consta…

01:28

A motorcycle of mass 100 k…

A 292-kg motorcycle is acc…

Okay, so this is a two part problem, um, with a motorcycle going across the hill where first we just have to find the centripetal force and all that is good, really good Require is us knowing the equation b squared over r and then plugging in the values that were given our mass 242 kilograms velocity. It's 25 meters per second, and nor radius is 126 meters. Plug it all in and you're gonna get ah, Hunt 1696 0.4, which is approximately 1.70 times 10 cubed. And the units are going to be new knees, the unit of force. All right, that's all that that there is to party. There's your first answer. Now let's move on to part B. And that asks us to find the total force on, um or start my bad, the normal force, the acts of the basically. Okay, So in this problem, we know that apart from being equal to the equation that we just found earlier, the centripetal force must be equal to mg minus. And and that's because if we look back toward drawing, we have our M G, which is gonna be pointing straight down. And we have a normal force who's been re pointing straight up. Now the normal force always points toward the center of our motion. But since we have our fn detracting from that are total centripetal force is going to be m G minus end. All right, if you want a normal force will have to do is rearrange that To get that end is equal to m g minus. Have a seat. Now we know our mass and, um, we could multiply that by the acceleration of gravity just 9.8 meters per second. And we just found our normal force or, I mean, are centripetal force. That's our 1.70 times 10 cubed Newtons. So we plugged it into a calculator and we solve and refined that n is equal to 1.656 times 10 cubed. And once again our units are going to be newness. And that's the answer to part B.

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