1. More on Newton’s 3 rd Law

2. 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.

3. 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!

4. Conceptual Example

5. 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.

6. Weight & Normal Force Weight  The force of gravity on an object. Write as F G  W. Consider an object in free fall. Newton’s 2 nd Law is: ∑F = ma If no other forces are acting, only F G (  W) acts (in the vertical direction). ∑F y = ma y Or: (down, of course) SI Units: Newtons (just like any force!). g = 9.8 m/s 2  If m = 1 kg, W = 9.8 N

7. “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: 2 nd Law  ∑F = ma = 0  There must be some other force acting besides gravity (weight) to have ∑F = 0. That force  Normal Force F N (= N in your text!) “Normal” is a math term for perpendicular (  ) F N is  to the surface & opposite to the weight (in this simple case only!) Caution!!! F N isn’t always = & opposite to the weight, as we’ll see!

8. Normal Force Where does the normal force come from?

9. Normal Force Where does the normal force come from? From the other object!!!

10. Normal Force Where does the normal force come from? From the other object!!! Is the normal force ALWAYS equal & opposite to the weight?

11. Normal Force Where does the normal force come from? From the other object!!! Is the normal force ALWAYS equal & opposite to the weight? NO!!!

12. F N 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 2 nd Law for Lincoln: F N – F G = 0 or F N = F G = mg Note! F N & F G AREN’T action-reaction pairs from N’s 3 rd Law! They’re equal & opposite because of N’s 2 nd Law! F N & F N ARE the action-reaction pairs!! Free Body Diagram Show all forces in proper directions. 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? The force exerted perpendicular to a surface is called the Normal Force F N.

13. Example Find: The normal force on the box from the table in Figs. a, b, c. Always use N’s 2 nd Law to CALCULATE F N ! The normal force is NOT always equal & opposite to the weight!! m = 10 kg

14. 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 F P > 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. F P – mg = ma 100 – 98 = 10a a = 0.2 m/s 2

15. Example : Apparent “weight loss” A 65-kg woman descends in an elevator that accelerates at 0.20g (= 1.96 m/s 2 ) 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 2 nd Law for her, ONLY the forces acting on her are included. By Newton’s 3 rd Law, the normal force F N acting upward on her is equal & opposite to the scale reading. So, the numerical value of F N is equal to the “weight” she reads on the scale! Obviously, F N here is NOT equal & opposite to her true weight mg!! How do we find F N ? As always We apply Newton’s 2 nd Law to her!!

16. Example : Apparent “weight loss” Mass m = 65-kg, mg = 637 N Acceleration a = 1.96 m/s 2 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 3 rd Law, the numerical value of F N is equal to the “weight” she reads on the scale! Obviously, F N is NOT equal & opposite to her true weight mg!! Find F N by applying Newton’s 2 nd Law to her!! Let down be positive so up is negative:  F y = ma  mg – F N = ma  F N = m(g – a) = (65)(9.8 – 1.96) = 509.6 N (F N /g)= 52 kg = Scale Reading in kg = “Effective Weight”!