Chapter 4: Newton s laws of motion

Transcription

1 Chapter 4: Newton s laws of motion Objectives: What are forces? How do we identify them? Drawing free-body diagrams. Relating forces and motion. Solving force and motion problems.

2 What is a force? Forces are vector quantities. A force has dimensions of. The common SI unit of force is a Newton (N). Contact forces are caused by objects interacting via direct contact. Examples: tension, friction, normal force. Long-range forces affect bodies that are separated even by empty space. Examples: gravitational force, Coulomb force.

3 Forces as vectors As with any set of vector quantities of equal dimension, forces may be summed together. In the xy-plane with the angle defined as sweeping counterclockwise from the +x-axis, the force,, can be broken down into the components The magnitude and direction may be found in the same manner as other vectors, where for for

4 Common contact forces Friction Normal Force Tension Force Spring Force

5 Mass and Weight w

6 The weight remains the same for all cases below

7 Newton s laws 1 st law: Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it. 2 nd law: The acceleration of an object is directly proportional to the net force acting on it, and is inversely proportional to the object s mass. The direction of the acceleration is in the direction of the net force acting on the object. 3 rd law: Whenever one object exerts a force on a second object, the second object exerts an equal force in the opposite direction on the first. For two objects:

8 Seat Belts: An Application of Newton s 1 st Law

9 Newton s 1 st law and head injuries Head strikes stationary object. Cranium stops abruptly. Brain continues moving and is compressed against skull.

10 A net force is A. the sum of the magnitudes of all the forces acting on an object. B. the difference between two forces that are acting on an object. C. the vector sum of all the forces acting on an object. D. the force with the largest magnitude acting on an object.

11 An action/reaction pair of forces A. point in the same direction. B. act on the same object. C. are always long-range forces. D. act oppositely so as to cancel each other

12 Acceleration and Newton s 2 nd law Newton s second law states that the sum of all forces is equal to the product of the object s mass and acceleration, This is a vector equation, which can be separated into components, The acceleration components follow as

13 A 40 ton car train travels along a straight track at a constant 40 mph. A typical skier kicks begins her descent down a hill. On which is the net force greater? A. The train. B. The skier. C. The net force is the same on both. D. There s not enough information to tell.

14 A constant force is exerted for a short time interval on a cart that is initially at rest on an air track. This force gives the cart a certain final speed. The same force is exerted for the same length of time on another cart, also initially at rest, that has twice the mass of the first one. The final speed of the heavier cart is 1. one-fourth 2. four times 3. half 4. double 5. the same as that of the lighter cart.

15 A constant force is exerted for a short time interval on a cart that is initially at rest on an air track. This force gives the cart a certain final speed. Suppose we repeat the experiment but, instead of starting from rest, the cart is already moving with constant speed in the direction of the force at the moment we begin to apply the force. After we exert the same constant force for the same short time interval, the increase in the cart s speed 1. is equal to two times its initial speed. 2. is equal to the square of its initial speed. 3. is equal to four times its initial speed. 4. is the same as when it started from rest. 5. cannot be determined from the information provided.

16 An object, when pushed with a net force F, has an acceleration of 2 m/s 2. Now twice the force is applied to an object that has four times the mass. Its acceleration will be A. ½ m/s 2. B. 1 m/s 2. C. 2 m/s 2. D. 4 m/s 2.

17 Reaction forces and Newton s 3 rd law When two objects interact, the two forces that they exert on each other are always equal in magnitude and opposite in direction, Application to the normal force of an object resting on a horizontal surface.

18 10-year-old Sarah stands on a skateboard. Her older brother Jack starts pushing her backward and she starts speeding up. The force of Jack on Sarah is A. greater than the force of Sarah on Jack. B. equal to than the force of Sarah on Jack. C. less than the force of Sarah on Jack.

19 A very large magnet is hung in front of an iron cart on a frictionless surface. Describe the subsequent motion. 1. Yes, to the right 2. Yes, to the left 3. No

20 What if I have a book on the table and put a second book on the first? Does the table need to push up more? 1. No. How would it know to do so? 2. Yes. It needs to hold up both books. 3. No. The reaction is to the book touching the table, not to both. 4. It depends on how gently you have put the second book down. 5. None of the above.

21 Mass B is greater than mass A. Force F acts via string #1; string #2 connects A and B. Which is true? 1. T 1 > T 2 2. T 2 > T 1 3. T 1 = T 2 B #2 A #1 F

22 Free body diagrams We are given a physical situation with forces acting on an object. Remove the object from the environment and identify the forces. A particle model may be used. Dashed lines are used to identify the components.

23 Examples of free body diagrams

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27 Example Boxes A and B are in contact on a horizontal, frictionless surface. Box A has mass 20.0 kg and box B has mass 5.0 kg. A horizontal force of 100 N is exerted on box A. What is the magnitude of the force that box A exerts on box B?