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Newton's Laws of Motion and Forces

Explore Newton's Third Law of Motion and how a force affects the motion of an object. Learn about impulse, momentum, and Newton's Second Law. Solve force and motion problems using free-body diagrams and equations.

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Newton's Laws of Motion and Forces

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  1. With his Third Law of motion, Isaac Newton observed the “double-ended” nature of any force. But he had also begun to examine how a force—or, more generally, a vector combination of forces, Fnet—affects the motion of any mass. He first de-scribed that in terms of its impulse—its effect upon momentum (Fnett = P), but then he restated it more usefully. First, notice that for any given (and constant) mass, its change in momentum is: P = Pf – Pi = mvf – mvi = m(vf – vi ) = mv So we can re-write the basic impulse-momentum relationship: Fnett = mv OSU PH 211, Before Class 14

  2. Now just re-arrange this algebraically: Fnet = mv/t But v/t is simply the average acceleration, aavg, of the object over the time interval t. And if we examine smaller and smaller increments of time, we arrive at a powerful instantaneous predictor of an object’s motion…. Newton’s Second Law: Fnet = dP/dt Fnet= d(mv)/dt For constant m: Fnet= md(v)/dt Fnet = ma At any given moment in time, the acceleration, a, of any mass, m, can be computed from the net force on that mass. OSU PH 211, Before Class 14

  3. A 90-kg skater gliding over level ice is being pushed by wind at his back with a force magnitude of 47.0 N. His skates experience a friction force magnitude of 20 N. What is the magnitude of his acceleration? 1. 0.222 m/s2 2.0.300 m/s2 3. 0.522 m/s2 4. 3.33 m/s2 5. None of the above. OSU PH 211, Before Class 14

  4. Draw and completely label the correct free-body diagram (FBD) for the previous situation (the skater blown by the wind). Let the skater be mass 1 (m1). This is the most useful form of visual representation (sketch) for solving force & motion problems. So… how do we “read” this diagram to get to equations to solve? FN.S1 Fk.S1 FAir.1 FG.E1 OSU PH 211, Before Class 14

  5. Every force is a vector, so Newton’s Second Law applies to each vector direction individually: Fx.net = max or: SFx = max Fy.net = maySFy = may The acceleration values revealed here—for as long as they remain steady—are ready-made for use in kinematic calculations. Now we can predict any object’s motion simply by knowing its mass and the net force acting upon it. OSU PH 211, Before Class 14

  6. Apply the above to the skater FBD: Write a set of correct equations (one for the x-direction, one for the y-direction) that relates the forces acting on the skater in the x- and y- directions to the x- and y- components of the skater’s acceleration. Here’s how: SF1.x = m1a1.x SF1.y = m1a1.y FAir.1 – Fk.S1 = m1a1.x FN.S1 – FG.E1 = m1a1.y FAir.1 – Fk.S1 = m1a1.x*FN.S1 – m1g = 0 *The third line of equations is where you put in the details about the forces and accelerations (but not numbers—except zero). There was nothing more to be said right now about the sum of the forces in the x-direction. But there was more detail about the y-forces: They sum to zero—because the acceleration in the y-direction is zero (the skater’s y-velocity remains constant at all times: vy = 0); and FG.E1 = m1g. How do we know that? (Read on…). OSU PH 211, Before Class 14

  7. Notice what Newton’s Second Law reveals about the force of gravity. Consider first a projectile of mass m (and let upward be defined as the positive y-direction): Fx.net = max = m(0) = 0 Fy.net = may = m(–g) = –mg The gravitational force, FG, acting on a projectile of mass m has a magnitude of mg (and is directed downward). Question: What is the gravitational force magnitude on an object of mass m when it’s not a projectile? Answer: The same as when it IS a projectil: mg . The earth doesn’t stop or change its pull on an object just because other forces are also acting on that object. OSU PH 211, Before Class 14

  8. According to Newton’s Second Law, if the net force in any direction on a body is zero, the body will have zero acceleration in that direction. This specific case is important enough to note with its own law…. Newton’s First Law: “An object’s motion will continue unchanged unless it is acted upon by a non-zero net force.” This was revolutionary in its day. It completely overturned the assumption (first enunciated by Aristotle) that the natural motion of an object was to come to rest. The above states the opposite. OSU PH 211, Before Class 14

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