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More on Newton’s rd 3 Law 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. 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! Conceptual Example 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. Weight & Normal Force Weight The force of gravity on an object. Write as FG W. • Consider an object in free fall. Newton’s 2nd Law is: ∑F = ma • If no other forces are acting, only FG ( W) acts (in the vertical direction). Or: ∑Fy = may (down, of course) • SI Units: Newtons (just like any force!). g = 9.8 m/s2 If m = 1 kg, W = 9.8 N “Normal” Force • Suppose an object is at rest on a table. No motion, but does the force of gravity stop? OF COURSE NOT! • But, the object does not move: 2nd Law ∑F = ma = 0 There must be some other force acting besides gravity (weight) to have ∑F = 0. • That force Normal Force FN (= N in your text!) “Normal” is a math term for perpendicular () FN is to the surface & opposite to the weight (in this simple case only!) Caution!!! FN isn’t always = & opposite to the weight, as we’ll see! Normal Force • Where does the normal force come from? Normal Force • Where does the normal force come from? • From the other object!!! Normal Force • Where does the normal force come from? • From the other object!!! • Is the normal force ALWAYS equal & opposite to the weight? Normal Force • Where does the normal force come from? • From the other object!!! • Is the normal force ALWAYS equal & opposite to the weight? NO!!! An object at rest must have no net force on it. If it is sitting on a table, the force of gravity is still there; what other force is there? Free Body Diagram Show all forces in proper directions. The force exerted perpendicular to a surface is called the Normal Force FN. FN is exactly as large as needed to balance the force from the object. (If the required force gets too big, something breaks!) ∑F = ma = 0 or Newton’s 2nd Law for Lincoln: FN – FG = 0 or FN = FG = mg Note! FN & FG AREN’T action-reaction pairs from N’s 3rd Law! They’re equal & opposite because of N’s 2nd Law! FN & FN ARE the action-reaction pairs!! Example The normal force is NOT always equal & opposite to the weight!! m = 10 kg Find: The normal force on the box from the table in Figs. a, b, c. Always use N’s 2nd Law to CALCULATE FN! Example What happens when a person pulls up on the box in the previous example with a force of 100.0 N? The box will accelerate upward because FP > mg!! Note: The normal force is zero in this case because the mass isn’t in contact with a surface. m = 10 kg ∑F = ma. FP – mg = ma 100 – 98 = 10a a = 0.2 m/s2 Example : Apparent “weight loss” A 65-kg woman descends in an elevator that accelerates at 0.20g (= 1.96 m/s2) downward. She stands on a scale that reads in kg. (a) During this acceleration, what is her weight & what does the scale read? (b) What does the scale read when the elevator descends at a constant speed of 2.0 m/s? • Note: To use Newton’s 2nd Law for her, ONLY the forces acting on her are included. By Newton’s 3rd Law, the normal force FN acting upward on her is equal & opposite to the scale reading. So, the numerical value of FN is equal to the “weight” she reads on the scale! Obviously, FN here is NOT equal & opposite to her true weight mg!! How do we find FN? As always We apply Newton’s 2nd Law to her!! Example : Apparent “weight loss” Mass m = 65-kg, mg = 637 N Acceleration a = 1.96 m/s2 down. (a) During acceleration, what is her weight & what does the scale read? (b) Answer part a if the elevator descends at a constant speed of 2.0 m/s? • Due to Newton’s 3rd Law, the numerical value of FN is equal to the “weight” she reads on the scale! Obviously, FN is NOT equal & opposite to her true weight mg!! Find FN by applying Newton’s 2nd Law to her!! • Let down be positive so up is negative: Fy = ma mg – FN = ma FN = m(g – a) = (65)(9.8 – 1.96) = 509.6 N (FN/g)= 52 kg = Scale Reading in kg = “Effective Weight”!