To study applications of Newton s Laws as they. To study conditions that establish equilibrium. To consider contact forces and the effects of

Transcription

1 Chap. 5: More Examples with Newton s Law Chap.5: Applying Newton s Laws To study conditions that establish equilibrium. To study applications of Newton s Laws as they apply when the net force is not zero. To consider contact forces and the effects of friction. To study elastic forces (such as spring force). To consider forces as they subdivide in nature (strong, electromagnetic, weak, and gravitational). 1 Formula Sheet for Exam 1 Repeat them for y. Note the vector nature, meaning x- and y- components. 2

2 Types of Force [II] Normal force (n, N, ) Tension (T, F T ) Weight (w, mg, F G ) Frictional force (f, F f ) spring force (F spr ) 3 Exam Problem is held in plane stay at rest Free-body diagram Newton s 2 nd law Friction, coefficient of friction 4

3 Exam Problem is held in plane stay at rest 5 Formula sheet Half-Time Free-body diagrams Solving a system of equations Free-body diagram Newton s 2 nd law 6

4 Modified Exam Problem? To open a new presentation of problem data in a free body diagram. To understand force either directly or as the net force of multiple components. To study and apply the concept of mass and acceleration as components of Newton s Second Law. Free-body diagram Newton s 2 nd law Friction, coefficient of friction 7 Things that we have to learn Free-body diagram Newton s 2 nd law Friction, coefficient of friction Motion F f Friction force on the block 8

5 Free-body diagram Newton s 2 nd law Kinetic Friction Force Friction, coefficient of friction Between two solid surfaces (Microscopic) bumps impede the motion Proportional to the magnitude of normal force: Motion F f = k where k = coefficient of kinetic friction F f Friction force on the block 9 Forces and Free Body Diagrams An example on page 103. The vertical components of forces are in equilibrium so there is no motion. This is a good example of forces in statics. Free Body Diagram is to identify all forces acted on a given body and to understand the motion. [Translation] Move forward, but speeding up, no motion in vertical [Translation] Move forward, but slowing down, no motion in vertical 10

6 Static and Kinetic Friction f s is less than s n until it starts moving (= static). 11 Static and Kinetic Friction f s is at maximum = s n f s is less than s n until it starts moving (= static). 12

7 Static and Kinetic Friction f k (= k n) < f s max (= s n) 13 s = 0.46 F T =??? N F f,s = 0.46 Just before moving Motion with constant v F f 14

8 s = 0.46 F f,s = 0.46 Just before moving F T =??? N Motion with constant v F f,k = k F f F f,s s 15 s = 0.46 F T =??? N F f,s = 0.46 Just before moving Motion with constant v F f,k = k F f F f,s s m a x (= 0) = F T F f,s m a y (= 0) = w 16

9 s = 0.46 F f,s = 0.46 Just before moving F T =??? N Motion with constant v F f,k = k F f F f,s s m a x (= 0) = F T 0.46 m a y (= 0) = s = 0.46 F T = 230 N F f,s = 0.46 Just before moving Motion with constant v F f,k = k F f F f,s s m a x (= 0) = F T 0.46 m a y (= 0) =

10 Just before moving F T = 230 N s = 0.46 k = 0.40 F f,s = 0.46 new step if the force is applied at an angle. F f,k = 0.40 F T =??? N Motion with constant v F f,k = k F f F f,s s m a x (= 0) = F T 0.46 m a y (= 0) = 500 m a x (= 0) = F T ( )0.40 m a y (= 0) = F T ( ) F T = 230 N s = 0.46 k = 0.40 new step if the force is applied at an angle. F T =??? N F f,s = 0.46 Just before moving F f,k = 0.40 Motion with constant v F f,k = k F f F f,s s m a x (= 0) = F T 0.46 m a y (= 0) = 500 m a x (= 0) = F T cos m a y (= 0) = F T sin

11 Just before moving F T = 230 N s = 0.46 k = 0.40 F f,s = 0.46 new step if the force is applied at an angle. F f,k = 0.40 F T = 188 N Motion with constant v F f,k = k F f F f,s s m a x (= 0) = F T 0.46 m a y (= 0) = 500 m a x (= 0) = F T cos m a y (= 0) = F T sin Formula sheet Half-Time Free-body diagrams Solving a system of equations m a x (= 0) = F T cos m a y (= 0) = F T sin Free-body diagram Newton s 2 nd law Friction, coefficient of friction 22

12 Modified Exam Problem To open a new presentation of problem data in a free body diagram. To understand force either directly or as the net force of multiple components. To study and apply the concept of mass and acceleration as components of Newton s Second Law. Free-body diagram Newton s 2 nd law Friction, coefficient of friction 23 Modified Exam Problem - Solution 24

13 Another Exam Problem To open a new presentation of problem data in a free body diagram. To understand force either directly or as the net force of multiple components. To study and apply the concept of mass and acceleration as components of Newton s Second Law. Free-body diagram Newton s 2 nd law Friction, coefficient of friction 25 Another Exam Problem Solution[1] Free-body diagram Newton s 2 nd law Friction, coefficient of friction 26

14 Another Exam Problem Solution[2] Free-body diagram Newton s 2 nd law Friction, coefficient of friction 27 28

15 29 Normal force (n, N, ) Tension (T, F T ) Weight (w, mg, F G ) Frictional force (f, F f ) spring force (F spr ) Types of Force 30

16 Stretch a spring to weigh objects. Figure 5.20 The force settings on the spring are calibrated with mass standards at normal earth gravity. The spring scales are often calibrated in force (N) and mass (kg). Find k. F spring = m g F spring = k d 31 Example 5 You are weighing 600 N on a bathroom scale containing a stiff spring. In equilibrium the spring is 1.0 cm under your weight. Find the spring constant k. Solution: Springs or other elastic material will exert force when stretched or compressed. Spring Force (Restoring Force): The spring exerts its force in the direction opposite the displacement. F S (x) = k x 32

17 Example 5 You are weighing 600 N on a bathroom scale containing a stiff spring. In equilibrium the spring is 1.0 cm under your weight. Find the spring constant k. Solution: Find the spring constant k k = F max / x max = (600 N) / (0.010 m) = 6.0 x 10 4 N/m 33 Example 6 A light spring having a force constant of 125 N/m is used to pull a 9.50 kg sled on a horizontal frictionless ice rink. If the sled has an acceleration of 2.00 m/s 2, by how much does the spring stretch if it pulls on the sled horizontally. What are they asking?. x Where do I get x?. F = k x Now I see k is given. So I need to know F to get x. Where can I get F?... F = m a 34

18 More Problems 35 Draw a Diagram FBD Newton s Laws Prob Free-body diagram Newton s 2 nd law Friction, coefficient of friction 36

19 Prob Draw a Diagram FBD Newton s Laws Free-body diagram Newton s 2 nd law Friction, coefficient of friction 37 Problem 9 (25 points): The coefficient of static friction between mass m 1 and the table is 0.400, whereas the coefficient of kinetic friction is (a) (5 pts) Draw the free-body diagram for each of m 1 and m 2. (b) (10 ps) Express the acceleration of the block in terms of m 1, m 2, and g. (c) (5 pts) What minimum value of m 1 will keep the system starting to move for m 2 = 2.00 kg? (d) (5 pts) What value(s) of m 1 will keep the system moving at constant speed for m 2 = 2.00 kg? 38

20 39 40

21 41 Two boxes, one with mass m 1 = 10.0 kg and the other with mass m 2 = 12.0 kg, sit on the frictionless surface, connected by a light rope (see the figure below). A motion is set by a pulling force F P = 40.0 N directed = 30.0 o above the horizontal. (a) (5 pts) draw free-body diagram for the 10.0-kg box; (b) (4 pts) draw the freebody diagram for the 12.0-kg box; (c) (16 pts) using the free-body diagrams and newton s 2 nd law to find tension on the rope, acceleration, and normal force on each of two boxes. 42

22 Quick Quiz: A heavy box rests on the horizontal bed of a truck. The truck driver starts the track and accelerates forward. Note a in the figure. Assume that contact surfaces between the box and the truck are rough, so that the box remains in the same position. Draw the free-body diagram for the box. a 43 Quick Quiz Solution: The friction force appears as it keeps from sliding back on the truck s bed. Thus, the direction of the (static) friction is pointing to the right. If you isolate the box, and draw the free-body diagram for the box, you find that it is consistent with Newtons 2 nd law: F a f m F f? Ignore the truck and two people! a F g F f is the force on the box by the truck s bed. F g 44

23 Quick Quiz Solution: The friction force appears as it keeps from sliding back on the truck s bed. Thus, the direction of the (static) friction is pointing to the right. If you isolate the box, and draw the free-body diagram for the box, you find that it is consistent with Newtons 2 nd law: Ff a m F f Ignore the truck and two people! a F f F g F f is the force on the box by the truck s bed. F g 45 Recap (Ch.4) : Free-Body Diagram (2D) Find the normal force on a 10-kg box sliding on desk (no friction) y Motion F P x F G Try P4.3 46

24 Example 6: Suppose that you are standing on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slide? a = 0.20 g 47 Example 6: Suppose that you are standing on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slide? a = 0.20 g x F f Which one is correct? F G F f Newton s 2 nd law: F = m a F f = m (0.20g) where F f = s = s (mg) Thus, s (mg) = m (0.20g) So, s =

25 There are a variety of force laws in nature. Strong interaction (g) Electromagnetic interactions () Weak interactions (W) Gravitational interactions (G) A holy grail of physics is the unified field theory. The goal will be to find the overriding principles that give rise to each of these very similar phenomena. 49 Elementary Particles and Foundamental Forces 12 elementary particles are known fundamental building blocks of matter. 4 fundamental forces govern the transitions between particles. The Standard Model, a mathematical rule, includes 12 particles and 3 forces. g W G strong force electromagnetic force weak force gravity Standard Model Cube All masses in MeV. ANIMAL MASSES SCALE WITH PARTICLE MASSES 50

26 Ordinary Matter: Atoms Quarks 10 cm Everything (that we can see) is made of electrons, up quarks and down quarks. 51 However, the Universe is made of... 3 Contents Dark Matter (23%) What is the dark matter? An elementary particle? Ordinary matter (4%) 52

27 Today s class Friction Spring force More Examples Summary of Chap. 5 Next class Chapter 6: Circular Motion and Gravitation 53 For Exam I The subjects are getting complicated. Thus, spending more time on PHYS201 is a key in general. Think of why biology and chemistry are the first science courses to be taught at high school, not physics. It is because math is heavily used in physics. Thus a study style for physics is different from biology and chemistry. How should I study? I worked on all MP problems. this is a very common question and worked on MP automatically doesn t mean you understand the subject. 1) Be a critical thinker. You will have to spent time to Understand Problem before you try to solve. What the problem is asking for? For example, can you draw a diagram? 2) Effective time management. Work on MP problems regularly, not try to finish in 2 days before exam. This allows you to write down your work on NOTE systematically. Not just on scratch paper. Such a note will be helpful for review. 3) Strengthen the weak subjects. Your NOTE will automatically give you a list of weak subjects. You could ask HELP efficiently to improve your readiness. 4) Textbook is your dictionary. Utilize it. Remember that the MP problems are the textbook problems. My exam problems are from the textbook. This means MP tries to lead you to utilize the textbook. It is like a dictionary. Find similar examples and see how problems are solved. 54