Last Time: Ch 3 Today: Relative Motion and Ch 4

Transcription

1 Last Time: Ch 3 Today: Relative Motion and Ch 4 Chapter 3 Finish Rela+ve Mo+on Chapter 4 Forces Newton s 1 st Law Newton s 2 nd Law Free body diagrams Examples (if we get that far)

2 Prelecture: Ques2on 2 A swimmer wishes to swim across the stream as shown. She knows she can maintain a constant speed v S = 0.4 m/s with respect to the water. The water in the stream moves with speed v W = 0.5 m/s as shown. Which of the following statements is true? a) She will not be able to cross the stream since v S < v W. b) She will be able to cross the stream but since v S < v W, she will never be able to reach any point upstream of X, but will be able to reach point X by choosing an appropriate heading. c) She will be able to cross the stream but since v S < v W, she will never be able to reach point X, no mauer what heading she chooses. a = swimmer b = water c = ground v ac = v ab + v bc

3 Checkpoint: Ques2on 1 A girl stands on a moving sidewalk (conveyor belt) that is moving to the right at a speed of 2 m/s rela+ve to the ground. A dog runs on the belt toward the girl at a speed of 8 m/s rela+ve to the belt. 1) What is the speed of the dog rela+ve to the ground? a) 6 m/s b) 8 m/s c) 10 m/s v dog, ground = v dog, belt + v belt, ground = (-8 m/s) + (2 m/s) = -6 m/s

4 What is the speed of the dog rela2ve to the girl? v dog,belt = 8 m/s Using the velocity formula: v dog, girl = v dog, belt + v belt, girl = - 8 m/s + 0 m/s = - 8 m/s v belt,ground = 2 m/s A) 6 m/s B) 8 m/s C) 10 m/s A) Because the girl is actually moving and the two vectors are opposite, so together they make 6 m/s B) Because the girl is not moving rela+ve to the belt, and the dog is going 8 m/s rela+ve to the belt, the dog is also moving 8 m/s rela+ve to the girl.. C) The dog and girl are running towards each other so when you add the two veloci+es together it would be 8+2.

5 Clicker Ques2on Three swimmers can swim equally fast rela+ve to the water. They have a race to see who can swim across a river in the least +me. Rela+ve to the water, Beth swims perpendicular to the flow, Ann swims upstream at 30 degrees, and Carly swims downstream at 30 degrees. Who gets across the river first? A) Ann B) Beth C) Carly Ann Beth Carly y x

6 Look at just water & swimmers Time to get across = D / V y B D A C 30 o 30 o y x V y,beth = V o V y,ann = V o cos(30 o ) V y,carly = V o cos(30 o )

7 Dynamics, forces, and Newton s Law s Chapter 4 Up to now we have been describing the kinema+cs of mo+on, how something moves. but what causes bodies to move the way that they do? The dynamics of mo+on - The rela+onship of mo+on to the forces that cause it 2 new concepts in Chapter 4 Force and Mass We will use force and mass to analyze the principles of dynamics, which are called Newton s laws of mo.on Newton s laws can be used to describe all the most familiar kinds of mo+on and are the founda+on of Classical Mechanics

8 What is a force?... A force is a push or a pull A force is an interac+on between two objects or between an object and its environment A force is a vector quan+ty, with a magnitude and direc9on The unit of force is the Newton [N] = kg m/s 2

9 Four Fundamental Forces

10 Common Forces (AKA the ones you care about)

11 Superposi2on of Forces The Principle of Superposi2on Any number of forces applied at a point on a body have the same effect as a single force equal to the vector sum of the forces. R = F 1 + F 2 + F = F R = F 1 + F 2

12 Superposi2on of Forces Any force can be replaced by its component vectors, ac+ng at the same point. R x = F x R y = F y

13 Example Net Force Two forces F 1 and F 2 act at a point. The magnitude of F 1 is 9.00N and its direc+on is 60.0 above the x- axis in the second quadrant. The magnitude of F 2 is 6.00N and its direc+on is 53.1 below the x- axis in the third quadrant. a) Where are the x- and y- components of the resultant force? b) What is the magnitude of the resultant force? F 1 = 9.00N II I F 2 = 6.00N III IV

14 Newton s 1 st Law A. An object at rest will remain at rest if the sum of the forces ac2ng on it are zero. B. If the resultant force ac2ng on a moving object is zero, the object will con2nue its mo2on at a constant velocity. What does that mean?!?... If there is no net force on an object then there is no change in the object s mo+on. F tot = 0 v(t) = v 0 = constant It s in equilibrium

15 Common Misconcep2on Let s visit one of our common misconcep+on about what happens when the total force on an object is zero. What happens when you push a puck across a table? Why does it stop? We really must be careful in analyzing whether or not the total force on an object is zero. What if we pushed it in space?

16 Mass and Iner2a The iner.a of an object is the tendency of that object to stay at rest, or for it to stay in mo+on with its original velocity. Mass is the quan+ta+ve measure of iner+a the more massive an object the greater force needed to deflect it from its current mo+on, or to get it moving in the first place.

17 Mass vs Weight Mass is a measure of iner+a Weight is a force due to gravity Ø These are not the same thing! Since g = 9.8 m s 2 on Earth Weight and mass are related w = mgĵ

18 Examples with weight A. What mass does 1 lb = N, correspond to on Earth? g Pluto = 0.54 m s 2 B. What about on Pluto where? C. What would the same mass weigh on Pluto?

19 Clicker Ques2on How much would a 250 lb person weight on Jupiter? A. 113 kg B lbs C. 663 lbs D. 250 lbs E. I have no idea w = mgĵ g = 9.8 m s 2 g Jupiter = 26 m s 2 1 lb = N

20 Newton s 2 nd Law Newton found that if you apply a force to an object then that object would experience an accelera+on in the direc+on of that force. This accelera+on was inversely propor+onal to the mass being acted on. F = ma Accelera.on is caused by a force; The bigger the mass, the harder this is to accomplish.

21 Pre- lecture: Ques2on 1 A force F acts on a mass M during the +me period from t = 0 to t = 1 s, the mass moves with velocity as shown v 1 Which of the following vectors best represents v 0, the velocity of mass M at t = 0?

22 Pre- lecture: Ques2on 1 A force F acts on a mass M during the +me period from t = 0 to t = 1 s, the mass moves with velocity as shown v 1 Which of the following vectors best represents mass M at t = 0? v 0, the velocity of

23 Clicker Ques2on A force F is applied to a small block, that pushes a larger block. The two blocks accelerate to the right. Compare the NET FORCE on the block with mass M, to the net force on the block with mass 5M. A) F M < F 5M B) F M = F 5M! F =! ma C) F M > F 5M Net Force Same accelera+on, so larger mass has larger net force. F M 5M a

24 Newton s 3 rd Law If body A exerts a force on body B (an ac+on), then body B exerts a force on body A ( a reac+on). These two forces have the same magnitude but are ac+ng in opposite direc9ons. The two forces act on different bodies.

25 Clicker Ques2on A small guy and a large football player moving at the same speed collide head- on. Which person experiences the larger accelera+on during the collision? A) The small guy. B) The football player. C) The accelera+ons are the same.

26 Clicker Ques2on A small guy moving at a high speed collides with a sta+onary large football player. Now, which person experiences the larger force during the collision? A) The small guy experiences the larger force. B) The football player experiences the larger force. C) Both experience the same force.

27 Pre- lecture: Ques2on 2 A car travelling at 70 mph down the interstate collides with a bug trying to cross the highway. Which of the following statements best describes this collision? A. The car exerts a larger force on the bug than the bug exerts on the car. B. The car exerts a smaller force on the bug than the bug exerts on the car. C. The car exerts the same sized force on the bug as the bug exerts on the car. D. The car exerts a force on the bug but the bug does not exert a force on the car. E. Neither exerts a force on the other. The bug gets smashed because it got in the way of the car.

28 Check Point: Ques2on 1 The net force on a box is in the posi+ve x direc+on. Which of the following statements best describes the mo+on of the box? A. Its velocity is parallel to the x axis. B. Its accelera+on is parallel to the x axis. C. Both its velocity and its accelera+on are parallel to the x axis. D. Neither its velocity nor its accelera+on need to be parallel to the x axis.

29 Check Point: Ques2on 2 You are driving a car around a circular track at a constant speed as shown above. The net force ac+ng on your car: A. Points radially inward, toward the center of the track. B. Points radially outward, away from the center of the track. C. Points forward, in the same direc+on you are moving. D. Points backward, opposite to the direc+on you are moving. E. Is zero.

30 Free- Body Diagrams

31 Free Body Diagrams a tool to help analyze Newton s Law problems Newton s 1 st and 2 nd laws apply to a specific body. Decide which body you are referring to. Only forces ac9ng on that body mauer. (don t get confused by forces the body is exer+ng on other things) Draw these forces ac+ng on the body as vectors at the point of applica+on of the force. Remember: Two forces of an ac+on- reac+on pair never appear in the same FBD (they act on different bodies) When you complete a FBD you should be able to iden+fy what other body is applying the force if you can t, you may be adding a non- existent force.

32 Clicker Ques2on A block sits at rest on a horizontal fric+onless surface. Which of the following sketches most closely resembles the correct free body diagram for all forces ac+ng on the block? Each arrow represents a force. (A) (B) (C) (D)

33 Example 2 blocks Two blocks, in contact with each other, move at a constant speed on a surface with fric+on. Draw free body diagrams for each block Find the force F in terms of the fric+on forces from each box. F m A m B (rough) F = m a