2 Dynamics: Newton’s Laws of Motion Newton’s First Law
3 Force Dynamics – connection between force and motion Force – any kind of push or pullrequired to cause a change in motion (acceleration)measured in Newtons (N)
4 Dynamics: Newton’s Laws of Motion Newton’s First Law of Motion
5 Newton’s First Law of Motion First Law – Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it.First Law – (Common) An object at rest remains at rest, and a object in motion, remains in motion unless acted upon by an outside force.
6 Newton’s First Law of Motion Newton’s Laws are only valid in an Inertial Frame of ReferenceFor example, if your frame of reference is an accelerating car – a cup in that car will slide with no apparent force being applied
7 Newton’s First Law of Motion An inertial frame of reference is one where if the first law is validInertia – resistance to change in motion
9 Mass Mass – a measurement of inertia A larger mass requires more force to accelerate itWeight – is a force, the force of gravity on a specific mass
10 Dynamics: Newton’s Laws of Motion Newton’s Second Law
11 Newton’s Second LawSecond Law – acceleration is directly proportional to the net force acting on it, and inversely proportional to its mass.-the direction is in the direction of the net forceEasier to see as an equationmore commonly written
12 SF – the vector sum of the forces Newton’s Second LawSF – the vector sum of the forcesIn one dimension this is simply adding or subtracting forces.
13 Free Body DiagramThe most important step in solving problems involving Newton’s Laws is to draw the free body diagramBe sure to include only the forces acting on the object of interestInclude any field forces acting on the objectDo not assume the normal force equals the weightF table on bookF Earth on book
15 Objects in Equilibrium Objects that are either at rest or moving with constant velocity are said to be in equilibriumAcceleration of an object can be modeled as zero:Mathematically, the net force acting on the object is zeroEquivalent to the set of component equations given by
16 Equilibrium, Example 1A lamp is suspended from a chain of negligible massThe forces acting on the lamp arethe downward force of gravitythe upward tension in the chainApplying equilibrium gives
17 Equilibrium, Example 2A traffic light weighing 100 N hangs from a vertical cable tied to two other cables that are fastened to a support. The upper cables make angles of 37 ° and 53° with the horizontal. Find the tension in each of the three cables.Conceptualize the traffic lightAssume cables don’t breakNothing is movingCategorize as an equilibrium problemNo movement, so acceleration is zeroModel as an object in equilibrium
18 Equilibrium, Example 2 Need 2 free-body diagrams Apply equilibrium equation to lightApply equilibrium equations to knot
19 Inclined PlaneSuppose a block with a mass of 2.50 kg is resting on a ramp. If the coefficient of static friction between the block and ramp is 0.350, what maximum angle can the ramp make with the horizontal before the block starts to slip down?
21 Multiple ObjectsA block of mass m1 on a rough, horizontal surface is connected to a ball of mass m2 by a lightweight cord over a lightweight, frictionless pulley as shown in figure. A force of magnitude F at an angle θ with the horizontal is applied to the block as shown and the block slides to the right. The coefficient of kinetic friction between the block and surface is μk. Find the magnitude of acceleration of the two objects.
22 We all remember the fun see-saw of our youth. Center of massWe all remember the fun see-saw of our youth.But what happens if . . .
23 Balancing Unequal Masses MoralBoth the masses and their positions affect whether or not the “see saw” balances.
25 Changing our Point of View The great Greek mathematician Archimedes said, “give me a place to stand and I will move the Earth,” meaning that if he had a lever long enough he could lift the Earth by his own effort.
26 We can think of leaving the masses in place and moving the fulcrum. In other words. . .We can think of leaving the masses in place and moving the fulcrum.It would have to be a pretty long see-saw in order to balance the school bus and the race car, though!
27 In other words. . .M1M2d1d2(We still) need:M1 d1 = M2 d2