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ssm A student is skatcboarding down a ramp that is 6.0 $\mathrm{m}$ long and inclined at $18^{\circ}$ with respect to the horizontal. The initial speed of the skateboarder at the top of the ramp is 2.6 $\mathrm{m} / \mathrm{s}$ . Neglect friction and find the speed at the bottom of the ramp.

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6.6 $\mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 4

Forces and Newton’s Laws of Motion

Newton's Laws of Motion

Applying Newton's Laws

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Simon Fraser University

Hope College

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.

01:14

A student is skateboarding…

04:16

02:47

03:12

02:24

A student is skateboar…

04:12

A skateboarder, with an in…

01:35

$$\begin{array}{l}{\te…

01:58

(II) A skateboarder, with …

09:32

A 6.60 -kg block slides wi…

02:29

A girl on a skateboard (to…

36:02

A boy of mass $60 \mathrm{…

01:24

Beginning from rest, an ob…

An 8.70 -kg block slides w…

02:58

SSM A skateboarder, starti…

A block slides down an inc…

02:49

Go The skateboarder in the…

to solve this question, we have to determine what is the acceleration off the state order. In order to do that, we have to apply Newton's second law in the direction off amusement. You will move in this direction, then are you choose that everything pointing there is positive and everything pointing to the other side is negative. Then, applying Newton's second law on this direction, we get the following The net force in that direction is the goes to the mass off the skateboarder times. He is acceleration in this direction. Then the net force has only one component, which is this component off the weight force that he called his weight acts component. And then we also have this other component which is not off our interest now, which would be the Y component off the wait for us. Then, in a direction of movement, we have the weight force component acts pointing to the positive direction and these composers and that force. Then it is equal to the mass times acceleration off the skate border. But the axe component off the weight force can be related to the weight force by using at the composition off the weight factor. To do that, we have to take a look here in this triangle so it's directed will try and go and then we have to discover one off its intern angles. To do that, we note the following This is 18 degrees. Then we can stretch the weight forced down here so that these is 90 degrees them. If this is 18 degrees, these is 90 degrees. Then this angle must be 90 miners. 18 which is it Cause to 72 The grease, Then the relation between the weight force on the X component can be given by the co sign off 72 degrees because they co sign after 72 degrees is equals Truth the agile. It's inside too. The axe component off the weight force divided by the high pattern use, which is the weight force. Then the X component off the weight force is equal to the weight forced times. The co sign off 72 degrees. Then here we have the weight force times. The co sign off 72 degrees equals to the mass times acceleration off the skate Werder. But remember that the weight forces given by the mass off the skate border times. That's original gravity, so M times G times Nico sign off 72 degrees is he goes to the mass times acceleration off escape border. Then we can simplify the masses to get an acceleration that is equals g times the co sign off. 70 Truth. Remember that G is approximately 9.8 meters per second squared. So here we have 9.8 times the co sign off 72 degrees, and this is his acceleration. But we have to get her mind. What is the final velocity? So what is the velocity of the skate border at the end off that ramp? In order to do that, we now use Torricelli's equation, which says the following the final velocity squared is he goes to the initial velocity squared, plus true times, acceleration times the distance. Then the squared is it goes to true 0.6 squared plus true times. The acceleration, which is 9.8 times the co sign off 72 degrees times displacement, which is six meters. Then the velocity is the coast to the square. It of true 0.6 squared plus two times 9.8 times the co sign off 72 degrees times six. This gives a final velocity off approximately 6.6 meters per second.

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