Chapter 4. Dynamics: Newton s Laws of Motion

Transcription

1 Chapter 4 Dynamics: Newton s Laws of Motion

2 Types of Forces: An Overview In nature there are two general types of forces, fundamental and nonfundamental. Fundamental Forces -- three have been identified, all other forces are derived from them. 1. Gravitational force (e.g. downward force on objects near the Earth s surface) 2. Strong Nuclear force (e.g. force that binds protons and neutrons together in the atomic nucleus) 3. Electroweak force (e.g. force between objects which are electrically charged)

3 Types of Forces: An Overview Examples of Nonfundamental Forces -- All of these are derived from the electroweak force: normal or support forces friction tension in a rope

4 The Gravitational Force Newton s Law of Universal Gravitation Every particle in the universe exerts an attractive force on every other particle. A particle is a piece of matter, small enough in size to be regarded as a mathematical point. The force that each exerts on the other is directed along the line joining the particles.

5 The Gravitational Force For two particles that have masses m 1 and m 2 and are separated by a distance r, the force has a magnitude given by F = G m m 1 r 2 2 G = N m 2 kg 2

6 The Gravitational Force Example. Find the gravitational force between a bicycle of mass 12 kg and a lawnmower of mass 25 kg sitting 1.2 m away from each other in a garden shed. F = G m 1 m 2 r 2 = ( N m 2 kg 2 ) ( 12 kg) ( 25 kg) ( 1.2 m) 2 = N very small, considering it takes a force of about 1 N to lift a pen!

7 Gravitational force between two Nimitz-class aircraft carriers Find the gravitational force between the two aircraft carriers pictured here. The mass of a Nimitz-class aircraft carrier is about 98,000 metric tons, and the separation between the aircraft carriers Is about 300 m. d = 300 m 1 metric ton =1000 kg 98,000 metric tons = kg F = G m 1 m 2 r 2 = G m2 d = # N m 2 % 2 $ kg 2 ( ) 2 & ( kg ' 300 m ( ) 2 = 7.1 N =1.6 lb

8 The Gravitational Force Even though the Earth and Moon are not point particles, because they are mostly spherical, Newton s law of Gravitation may be applied using the distance between their centers as if they were point particles.

9 The Gravitational Force Find the average gravitational force between The Earth (mass = 5.98 x kg) and Moon (mass = 7.35 x kg) if their mean distance apart is 3.85 x 10 8 m. F = GM M M E /r 2 = (6.67 x )(7.35 x )(5.98 x )/(3.85 x 10 8 ) 2 = 1.98 x N very large!

10 The Gravitational Force Definition of Weight The weight of an object on or above the earth is the gravitational force that the earth exerts on the object. The weight always acts downwards, toward the center of the earth. On or above another astronomical body, the weight is the gravitational force exerted on the object by that body. SI Unit of Weight: newton (N)

11 The Gravitational Force The weight, W, of an object can be associated with its mass, m, using Newton s 2 nd law: +y Σ F y = -W = ma y = m(-g) m --> W = mg a y = -g W

12 The Gravitational Force Relation Between Mass and Weight W = G M E r m 2 W = mg g = G M r E 2 The acceleration of gravity depends on the mass of the planet and the distance from its center.

13 The Gravitational Force On the earth s surface: g = G M E R E 2 ( ( ) kg) ( m) 2 = N m 2 kg 2 = 9.80 m s 2

14 Types of Forces: An Overview Examples of Nonfundamental Forces -- All of these are derived from the electroweak force: normal or support forces friction tension in a rope

15 The Normal Force Definition of the Normal Force The normal force is one component of the force that a surface exerts on an object with which it is in contact namely, the component that is perpendicular to the surface. Weight is the downward force exerted by gravity on an object. For a block of weight W sitting at rest on a table, from Newton s 2 nd law: Σ F y = F N - W = ma y = 0 --> F N = W, and is directed upward

16 The Normal Force Σ F = F N + F H + W = 0 F N 11 N 15 N = 0 F N = 26 N F N + 11 N 15 N = 0 F N = 4 N

17 The Normal Force Apparent Weight The apparent weight of an object is the reading of the scale. It is equal to the normal force the scale exerts on the man.

18 The Normal Force Sum of the forces acting on the man: W Fy = + FN mg = ma F = mg + N ma apparent weight true weight From Newton s 3rd law: the normal force exerted by the scale on the man is equal (and opposite) to the force the man exerts on the scale --> the man s apparent weight

19 Find the acceleration in each case: F N = mg + ma a = F mg N m Since W = mg = 700 N m = 700 N = 71.4 kg m s a = F N ( m s 2 ) F N = 700 N a = F N =1000 N = 0 m a = s = 4.20 m s 2 F N = 400 N a = = 4.20 m s 2 F N = 0 N a = = 9.80 m s 2