W4.4 - Physics for Scientists&Engineers 1 1 Physics for...

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Unformatted text preview: January 30, 2008 Physics for Scientists&Engineers 1 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Spring Semester 2008 Lecture 15 January 30, 2008 Physics for Scientists&Engineers 1 2 Newton Newton ’ ’ s Three Laws s Three Laws Newton’s First Law: • In the absence of an external force on an object, this object will remain at rest, if it was at rest, or, if it was moving, it will remain in motion with the same velocity. Newton’s Second Law: • If there is a net external force acting on an object with mass , then the force will cause an acceleration, : Newton’s Third Law: • `The forces that two interacting objects exert on each other are always exactly equal in magnitude and opposite in direction to each other. ! F net ! F net = m ! a ! a ! F 1,2 = ! ! F 2,1 m January 30, 2008 Physics for Scientists&Engineers 1 3 Yesterday: Inclined Plane Yesterday: Inclined Plane • Step 1: pick coordinate system such that x-axis is along plane • Step 2: y-component has no acceleration => determines normal force • Step 3: Use Newton’s Second Law to determine accelerationin x-direction • Please note that the mass of the object has canceled out of this equation => All objects accelerate at the same rate on this plane, independent of their mass. • We can write down the equation for the acceleration vector: • Limiting case: acceleration approaches 0 as angle approaches 0. Expected! F x = ma x ! a x = g sin " ! a = ( g sin ! ) ˆ x F y = ! N = mg cos " ! ! N ! F g ! mg cos ! mg sin ! x y January 30, 2008 Physics for Scientists&Engineers 1 4 Friction Friction Introduction of a new force: friction Friction forces are present in practically all kinematical processes Concerning friction we observe the following • If an object is at rest, then it takes a threshold of an external force to make it move ( experiment 1 experiment 1 ) • If an object is at rest, then the force one must exert to start it moving is larger than the force required to keep it moving ( experiment 2 experiment 2 ) • The friction force is proportional to the normal force ( experiment 3 experiment 3 ) • The friction force is independent of the size of the contact area ( experiment 4 experiment 4 ) • The friction force depends on the roughness of the contact surface ( experiment 5 experiment 5 ) January 30, 2008 Physics for Scientists&Engineers 1 5 Two Types of Friction...
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W4.4 - Physics for Scientists&Engineers 1 1 Physics for...

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