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A 292-kg motorcycle is accelerating up along a ramp that is inclined $30.0^{\circ}$ above the horizontal. The propulsion force pushing the motorcycle up the ramp is $3150 \mathrm{N},$ and air resistance produces a force of 250 $\mathrm{N}$ that opposes the motion. Find the magnitude of the motorcycle's acceleration.

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5.03 $\mathrm{m} / \mathrm{s}^{2}$

Physics 101 Mechanics

Chapter 4

Forces and Newton’s Laws of Motion

Newton's Laws of Motion

Applying Newton's Laws

Hope College

University of Sheffield

University of Winnipeg

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.

02:52

A 292-kg motorcycle is acc…

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02:40

A 328-kg motorcycle is acc…

04:06

A powerful motorcycle can …

01:50

03:27

A motorcycle and $60.0 \ma…

03:13

A motorcycle and 60.0 kg r…

01:20

A net force of $265 \math…

03:23

A motorcycle (mass of cycl…

03:48

A bicycle and $50.0$ -kg r…

02:36

A 20.0 -kg sled is being p…

04:10

A body of mass 2.00 kg is …

00:47

(I) A net force of 265 $\m…

to solve this question, we can apply Newton's second law in the direction off the movement. So the movement happens in this direction. Let me say that everything that is pointing there, it's positive, and everything that is pointing to the opposite side is negative as a consequence. Then applying Newton's second law in this direction, let me call it the X direction we get the following than that force is equal to the mass off the motorcycle times Its acceleration then in that force has three components. He's one which is a positive component 3150 minus these one, which is a negative component because it points the negative X direction. And then we have apart off the weight force because the weight force could be the composer in two components. These one and these one let me cold. These the acts component and is the y component. We care about the X component for now. So the X component acting there in the opposite direction after amusement. So it is negative. So miners. But will you x. This is because of the mass off the motorcycle times its acceleration. Then how can it? Coakley to the X component off. The weight force knows the following these angle here is started agrees. Right now, let me extend the weight force to form another triangle. These one, then this is a 90 degree angle before this must be a 60 degree angle. Now note that the Y component off the weight force makes 90 degrees. If the surface, then if they make 90 degrees on this 60 degrees, these must be 30 degrees. Then this angle is 30 day grace, too. Now, to calculate what is the X component, we can use the sign off 30 degrees because the sign off 30 degrees in that context is given by the opposite side off the triangle. I'm talking about this triangle. Sure, the opposite side is the X component off the weight force divided by the high party news, which is the magnitude of the weight force. Then the X component off the weight force is It goes to the magnitude of the weight force times this sign off 30 degrees, which is 1/2 So W X is he coast to know where you divide it. By true, the weight forces given by the mass off the motorcycle times acceleration of gravity near the surface off the earth. Then we have these equations. Also remember that G is approximately 9.8 meters per second squared, then going back to our equation. We have 3150 minus 250 miners. 292 times 9.8. Divided lecture is ecos to 292 times acceleration. Then we can solve this equation for the acceleration as the acceleration is the cost to this mind is this Miners D's times in 9.8, divided by True is 4.9 and these world thing is divided by 292. These results in an acceleration of approximately five 0.3 meters per second squared.

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