Newtons Second Law Lab Inertia Mass Inertia The
Newton’s Second Law (Lab)
Inertia & Mass • Inertia The tendency of an object to maintain its state of rest or motion. • MASS: A measure of the inertia of an object – Quantity of matter in a body – Quantify mass by having a standard mass = Standard Kilogram (kg) (Similar to standards for length & time). – SI Unit of Mass = Kilogram (kg) • cgs unit = gram (g) = 10 -3 kg • Weight: (NOT the same as mass!) – The force of gravity on an object (later in the chapter).
Newton’s Second Law • 1 st Law: If no net force acts on it, an object remains at rest or in uniform motion in straight line. • What if a net force does act? Do Experiments. • Find, if the net force ∑F 0 The velocity v changes (in magnitude, in direction or both). • A change in the velocity v (Δv) There is an acceleration a = (Δv/Δt) OR A net force acting on a body produces an acceleration!! ∑F a
• Experiment: The net force ∑F on a body and the acceleration a of that body are related. • HOW? Answer by EXPERIMENTS! – Thousands of experiments over hundreds of years find (for an object of mass m): a ∑F/m (proportionality) • We choose the units of force so that this is not just a proportionality but an equation: OR: a ∑F/m (total!) ∑F = ma
• Newton’s 2 nd Law: ∑F = ma ∑F = the net (TOTAL!) force acting on mass m m = the mass (inertia) of the object. a = acceleration of the object. a is a description of the effect of ∑F ∑F is the cause of a. • To emphasize that the F in Newton’s 2 nd Law is the TOTAL (net) force on the mass m, your text writes: ∑F = ma Vector Sum of all Forces! ∑ = a math symbol meaning sum (capital sigma)
• Newton’s 2 nd Law: Based on experiment! Not derivable ∑F = ma mathematically!! A VECTOR equation!! Holds component by component. ∑Fx = max, ∑Fy = may, ∑Fz = maz ONE OF THE MOST FUNDAMENTAL & IMPORTANT LAWS OF CLASSICAL PHYSICS!!!
Summary Newton’s 2 nd law is the relation between acceleration & force. Acceleration is proportional to force and inversely proportional to mass. It takes a force to change either the direction of motion or the speed of an object. More force means more acceleration; the same force exerted on a more massive object will yield less acceleration.
Now, a more precise definition of force: Force = an action capable of accelerating an object. Force is a vector & is true along each coordinate axis. The SI unit of force is the Newton (N) ∑F = ma, unit = kg m/s 2 1 N = 1 kg m/s 2 Note The pound is a unit of force, not of mass, & can therefore be equated to Newtons but not to kilograms!
Examples Example: Estimate the net force needed to accelerate (a) a 1000 -kg car at (½)g (b) a 200 -g apple at the same rate. Example: Force to stop a car. What average net force is required to bring a 1500 -kg car to rest from a speed of 100 km/h (27. 8 m/s) within a distance of 55 m?
Example 5. 1: Accelerating Hockey Puck A hockey puck, mass m = 0. 3 kg, slides on the horizontal, frictionless surface of an ice rink. Two hockey sticks strike the puck simultaneously, exerting forces F 1 & F 2 on it. Calculate the magnitude & direction of the acceleration. Steps to Solve the Problem 1. Sketch the force diagram (“Free Body Diagram”). 2. Choose a coordinate system. 3. Resolve Forces (find components) along x & y axes. 4. Write Newton’s 2 nd Law equations x & y directions. 5. Use Newton’s 2 nd Law equations & algebra to solve for unknowns in the problem. x & y directions.
Example Find the resultant force FR
Example Find the resultant force FR FR = [(F 1)2 + (F 2)2](½) = 141 N tanθ = (F 2/F 1) = 1, θ = 45º
Example Find the resultant force FR If the boat moves with acceleration a, ∑F = FR = ma FRx = max, FRy = may
Sect. 5. 5: Gravitational Force & Weight • Weight Force of gravity on an object. Varies (slightly) from location to location because g varies. Write as Fg mg. (Read discussion of difference between inertial mass & gravitational mass). • Consider an object in free fall. Newton’s 2 nd Law: ∑F = ma • If no other forces are acting, only Fg mg acts (in vertical direction). ∑Fy = may or Fg = mg (down, of course) • SI Units: Newtons (just like any force!). g = 9. 8 m/s 2 If m = 1 kg, Fg = 9. 8 N
Newton’s 3 rd Law • 2 nd Law: A quantitative description of how forces affect motion. • BUT: Where do forces come from? – EXPERIMENTS find: Forces applied to an object are ALWAYS applied by another object. Newton’s 3 rd Law: “Whenever one object exerts a force F 12 on a second object, the second object exerts an equal and opposite force -F 12 on the first object. ” – Law of Action-Reaction: “Every action has an equal & opposite reaction”. (Action-reaction forces act on DIFFERENT objects!)
Another Statement of Newton’s 3 rd Law “If two objects interact, the force F 12 exerted by object 1 on object 2 is equal in magnitude & opposite in direction to the force F 21 exerted by object 2 on object 1. ” As in figure
Example: Newton’s 3 rd Law When a force is exerted on an object, that force is caused by another object. Newton’s 3 rd Law: “Whenever one object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first. ” If your hand pushes against the edge of a desk (the force vector shown in red), the desk pushes back against your hand (this force vector is shown in purple, to remind us that this force acts on a DIFFERENT object).
Newton’s 3 rd Law: Alternative Statements 1. Forces always occur in pairs 2. A single isolated force cannot exist 3. The “action force” is equal in magnitude to the “reaction force” & opposite in direction a. One of the forces is the “action force”, the other is the “reaction force” b. It doesn’t matter which is considered the “action” & which the “reaction” c. The action & reaction forces must act on different objects & be of the same type
Conceptual Example: What exerts the force to move a car?
Conceptual Example: What exerts the force to move a car? Response A common answer is that the engine makes the car move forward. But it is not so simple. The engine makes the wheels go around. But if the tires are on slick ice or deep mud, they just spin. Friction is needed. On firm ground, the tires push backward against the ground because of friction. By Newton’s 3 rd Law, the ground pushes on the tires in the opposite direction, accelerating the car forward.
Helpful notation: On forces, the 1 st subscript is the object that the force is being exerted on; the 2 nd is the source. Action-Reaction Pairs act on Different Objects!
Action-Reaction Pairs: Act on Different Objects The key to correct the application of Newton’s 3 rd Law is: The forces are exerted on different objects. Make sure you don’t use them as if they were acting on the same object. Example: When an ice skater pushes against the railing, the railing pushes back & this reaction force causes her to move away.
Conceptual Example Michelangelo’s assistant has been assigned the task of moving a block of marble using a sled. He says to his boss, “When I exert a forward force on the sled, the sled exerts an equal and opposite force backward. So how can I ever start it moving? No matter how hard I pull, the backward reaction force always equals my forward force, so the net force must be zero. I’ll never be able to move this load. ” Is he correct?
Action-Reaction Pairs Act On Different Objects • Forces exerted BY an object DO NOT (directly) influence its motion!! • Forces exerted ON an object (BY some other object) DO influence its motion!! • When discussing forces, use the words “BY” and “ON” carefully.
Rocket propulsion can be explained using Newton’s Third Law: Hot gases from combustion spew out of the tail of the rocket at high speeds. The reaction force is what propels the rocket. Note: The rocket doesn’t need anything to “push” against.
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