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Chapter 4 Dynamics Newton’s Laws of Motion Force: What is it? • Force = any kind of a push or a pull on an object. • To exert a force = to put a push or pull on an object. Force: What does it do? • If an object is at rest, it takes force to get it moving. • If an object is already moving, a force will change its velocity, either in direction or magnitude. • In short, to accelerate an object, a force is required. • We can define force as an action capable of accelerating an object. Force as a vector • Picture a box on the floor. • How many ways can I make the box move? • How many different directions can I move the box? • Force is a vector, it has a magnitude (how hard I push or pull) and a direction (where I push or pull). Aristotle’s view • Back in ancient Greece, Aristotle observed that the only way to move an object was to push or pull it. • He argued that an object’s natural state was to be at rest. • He also argued the greater the force the greater its speed. • This idea lasted 2000 years! Along comes Galileo • Galileo comes around and argues that it is just as natural for an object to be in horizontal motion with a constant velocity. • After 2000 years of Aristotle, Galileo must have some powerful proof right? Some creative experiment that disproves Aristotle or something. Actually… • …Not really, all Galileo had was this: • Imagine a heavy block pushed across a rough surface. • Now picture the same block pushed across a smooth surface. • What changes? • Now picture a surface that does not rub against the block at all. Why is Aristotle Mistaken? • We already said that to change velocity, a force is required. • So to slow an object down requires a force. • The only reason you have to keep pushing an object is to overcome the force of friction. • More on what that means soon, but first, introducing… Newton’s 3 laws of motion: the 1st law • Isaac Newton was the first scientist to actually produce the evidence to support Galileo’s idea. • It was his work that resulted in 3 famous laws, the 1st being the following: • An object in motion stays in motion, or an object at rest stays at rest, until acted upon by an outside force. Inertia • Some objects change speed or direction easily and some objects do not. • The ability of an object to maintain its velocity is called inertia. Newton’s 2nd Law • Everything we just covered goes into Newton’s 2nd law. • A force will give a bigger mass less acceleration than a smaller mass. • This is explained in the following law: F ma F ma • • • • ΣF means the sum of all forces m = mass a = acceleration By sum of all forces I mean that multiple forces can work with or against each other Units of Force • In honor of Newton, the unit of force is called a newton, N. • 1N is defined as the amount of push it takes to give a 1kg object an acceleration of 1m/s2 • So 1N = 1kgm/s2 Example • Estimate the force needed to accelerate a 1000kg at ½g and a 200-g apple at the same rate. Solution • Car: m = 1000kg, a = 1/2g, which is about 5m/s2 • ΣF = ma = 1000kg x 5m/s2 = 5000kgm/s2 = 5000N • Apple: m = 200g = 0.2kg, a = 5m/s2 • ΣF = ma = 0.2kg x 5m/s2 = 1kgm/s2 = 1N Example • What force is needed to bring a 1500kg car to rest from a speed of 100km/h within a distance of 55m? Solution • We will need to use ΣF = ma, but first we will need to find the acceleration. • So let’s look at what we got: v0 = 100km/h, v = 0km/h, x0 = 0, and x = 55m • So we need to use, v2 = v02 + 2a(x – x0) and solve for a, v v 0 28m / s 2 a 7.1m / s 2x x0 255m 2 2 0 2 Solution part 2 • Finally we can use ΣF = ma • ΣF = ma = (1500kg)(-7.1m/s2) = -11000N or 1.1 x 104 N Cyclops • • • • Name: Scott Summers Team: The X – men Code name: Cyclops Abilities: Can shoot beams of “pure force” from his eyes. • Question: Why doesn’t Scott’s head fly off when he fires a beam? Newton’s 3rd Law • Newton’s 3rd law is this: Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. • This law is also restated as “forces always come in pairs”. • Imagine a book on a table. Gravity pulls it down and the table pushes it back up. Back to Cyclops • When Scott Summers forces a beam from his eyes, the beam should but a force back on Scott. • And not just any force but an equal force in the opposite direction. • According to Newton, either Scott should fly back when he fires a beam, or his head should be ripped from his body. Applications of Newton’s 3rd • This law is extremely important. • It is what let’s us walk, it makes cars go forward, and it puts rockets into space. • Your foot puts a force on the ground and the ground puts an equal force back on you (friction), which pushes you forward. • Ditto for the car’s tires. • In a rocket, expanding gas is pushed down out of the rocket, the gas pushes back on the rocket sending it up.