Newton’s Second Law (Lab)

(Similar to standards for length & time). 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).

A net force acting on a body produces an acceleration!! ∑F  a Newton’s Second Law 1st 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

a  ∑F/m (proportionality) 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: a  ∑F/m OR: (total!)  ∑F = ma

∑F is the cause of a. ∑F = ma Newton’s 2nd 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 2nd Law is the TOTAL (net) force on the mass m, your text writes: ∑F = ma ∑ = a math symbol meaning sum (capital sigma) Vector Sum of all Forces!

ONE OF THE MOST FUNDAMENTAL & IMPORTANT LAWS OF CLASSICAL PHYSICS!!! Newton’s 2nd Law: ∑F = ma A VECTOR equation!! Holds component by component. ∑Fx = max, ∑Fy = may, ∑Fz = maz ONE OF THE MOST FUNDAMENTAL & IMPORTANT LAWS OF CLASSICAL PHYSICS!!! Based on experiment! Not derivable mathematically!!

Summary Newton’s 2nd 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. Figure 4-5. Caption: The bobsled accelerates because the team exerts a force.

Force = an action capable of accelerating an object. 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/s2  1N = 1 kg m/s2 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? Figure 4-6. 4-2. Use Newton’s second law: acceleration is about 5 m/s2, so F is about 5000 N for the car and 1 N for the apple. 4-3. First, find the acceleration (assumed constant) from the initial and final speeds and the stopping distance; a = -7.1 m/s2. Then use Newton’s second law: F = -1.1 x 104 N.

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 F1 & F2 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 2nd Law equations x & y directions. 5. Use Newton’s 2nd 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 = [(F1)2 + (F2)2](½) = 141 N tanθ = (F2/F1) = 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 2nd 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/s2  If m = 1 kg, Fg = 9.8 N

Newton’s 3rd Law 2nd 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 3rd Law: “Whenever one object exerts a force F12 on a second object, the second object exerts an equal and opposite force -F12 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 3rd Law “If two objects interact, the force F12 exerted by object 1 on object 2 is equal in magnitude & opposite in direction to the force F21 exerted by object 2 on object 1.” As in figure

Example: Newton’s 3rd Law When a force is exerted on an object, that force is caused by another object. Newton’s 3rd 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 3rd 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 3rd Law, the ground pushes on the tires in the opposite direction, accelerating the car forward.

Action-Reaction Pairs act on Different Objects! Helpful notation: On forces, the 1st subscript is the object that the force is being exerted on; the 2nd is the source. Action-Reaction Pairs act on Different Objects! Figure 4-11. Caption: We can walk forward because, when one foot pushes backward against the ground, the ground pushes forward on that foot (Newton’s third law). The two forces shown act on different objects.

Action-Reaction Pairs: Act on Different Objects The key to correct the application of Newton’s 3rd 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.

Note: The rocket doesn’t need anything to “push” against. 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. Figure 4-10. Caption: Another example of Newton’s third law: the launch of a rocket. The rocket engine pushes the gases downward, and the gases exert an equal and opposite force upward on the rocket, accelerating it upward. (A rocket does not accelerate as a result of its propelling gases pushing against the ground.)