# Ch.4 Forces. Conceptual questions #1, 2, 12 Problem 1, 2, 5, 6, 7, 10, 12, 15, 16, 19, 20, 21, 23, 24, 26, 27, 30, 38, 39, 41, 42, 47, 50, 56, 66

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1 Ch.4 Forces Conceptual questions #1, 2, 12 Problem 1, 2, 5, 6, 7, 10, 12, 15, 16, 19, 20, 21, 23, 24, 26, 27, 30, 38, 39, 41, 42, 47, 50, 56, 66

2 Forces Forces - vector quantity that changes the velocity vector of an object. When you hit a baseball, the velocity of the ball changes. Can be a push or a pull on an object Contact forces result from physical contact with an object (pulling a trailer, friction forces, normal force) Field forces interactions where contact is not necessary (electric force, gravitational force)

3 4 fundamental forces Strong nuclear force subatomic particles Electromagnetic forces forces between charges Weak nuclear force radioactive decay Gravitational force attraction between objects with mass (why a dropped ball falls down)

4 Newton s Laws 3 Laws that govern the motion of a particle 1 st Law 2 nd law 3 rd Law

5 Newton s 1 st Law Also called law of inertia. Objects at rest stay at rest, objects in motion continue that motion, unless influenced by an outside force. Book s definition: An object moves with a velocity that is constant in magnitude and direction, unless acted on by a nonzero net force.

6 Mass and inertia Inertia the tendency of an object to continue in its original state of motion. Mass measurement of an object s resistance to change in motion due to a force. The more massive an object, the more inertia the object will have. An 18-wheeler has a lot more inertia than a small car. It s harder to stop the 18-wheeler.

7 Determining Inertia/Mass We measure the mass of an object. The U.S. unit is the slug The SI unit is kilogram (kg) We will exclusively use the SI units mass of a small car ~1000 kg mass of a cat ~4 kg mass of a penny ~1 gm

8 The more mass an object has, the more force is needed to change it s velocity (accelerate the object). Kick a volleyball it will move a lot Kick a bowling ball it won t move as much The bowling ball resists changing its velocity more than the volleyball. The bowling ball has more inertia (a higher mass).

9 Book s definition: Newton s 2 nd Law The acceleration, a, of an object is directly proportional to the net force acting on it and inversely proportionally to its mass. equation: a = F/m or: F = ma, the, here means the sum of the forces, or the adding up of all the force vectors which are exerted on an object.

10 Newton s 2 nd Law Remember that F = ma, is a vector equation. We can write the 2 nd law with 3 component equations. F x = ma x F y = ma y F z = ma z The 2 nd law can be applied in the 3 dimensions individually. If there is no net force, the acceleration is zero, then the velocity is constant.

11 Newton s 3 rd Law Book definition: If object 1 and object 2 interact, the force F 12 exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force F 21 exerted by object 2 on object 1. Law of equal and opposite reaction (If you push on a wall, the wall pushes back onto you.)

12 Quick Quiz #4.1

13 Units of forces Units of forces are the pound (US) and the newton (SI). We will use the newton. 1 N = 1 kg m/s 2 To convert: 1 N = lb 1 lb = 4.45 N Also of use: 1 kg of mass weighs 2.2 lbs.

14 Notice that the weight is equal to mass x gravity A 200 pound person weighs 890 N. 1kg 200lbs 9.8m / s 2 890N 2.2lbs (9.8/2.2 gives us the 4.45 used to convert from pounds to newtons)

15 Some weights in newtons Weight of a truck, 5000 lbs 1kg 5000lbs 9.8m / s N 2.2lbs Or 22 kn Weight of Earth. Mass of Earth is 5.98x10 24 kg So its weight is (5.98x10 24 kg)(9.8m/s 2 ) = 5.86x10 25 N N

16 Example The propeller of a boat motor exerts a force of 200 N on 500 kg boat. What will the boat s acceleration be? Use 2 nd Law 200 N = (500 kg)a F = ma a = (200 N)/(500kg) = 0.4 m/s 2 What if the boat s mass doubled (m = 1000 kg)? a = (200 N)/(1000 kg) = 0.2 m/s 2

17 Examples of forces we will work with Gravitational force due to gravity Normal force due to contact Friction forces Spring forces compressing or stretching a spring Tensions involving ropes, cables

18 Gravitational force Gravitational force is the mutual attraction between any two objects in the Universe. Determined by F g = Gm 1 m 2 /r 2 (r is the separation between the two objects) Gravitational constant G = 6.67 x Nm 2 /kg 2 We will use this more later.

19 Gravitational Force F g = Gm a m b /r 2 Letting m b equal the mass of the Earth and r the radius of the Earth we get: F g = (6.67 x Nm / kg )(5.98 x (6.38 x10 m) 24 kg) m b F g = (9.8 m/s 2 )m b = m b g Weight w = mg, where g = Gm E /r 2

20 Gravitational Force Find the weight of a 100 kg person standing at: Sea level. r = r e = 6.38x10 6 m On top of Mt. Everest r = r e m In spacecraft 5x10 6 m above Earth, r = 11.38x10 6 m

21 Sea level: r = r e = 6.38x10 6 m w = m p g = m p (Gm E /r 2 ) = 100 kg(9.8m/s 2 ) w = 980 N (220.2 lbs) Mt. Everest: r = r e m = 6.39x10 6 m w = m p g = m p (Gm E /r 2 ) = 100 kg(9.77m/s 2 ) w = 977 N (219.5 lbs) Spacecraft: r = 11.38x10 6 m w = m p g = m p (Gm E /r 2 ) = 100 kg(3.08m/s 2 ) w = N (69.2 lbs)

22 On the Moon On the surface of the moon, g = g moon =1.62m/s 2 What would a 100 kg person weigh on the moon? w = (100kg)(1.62m/s 2 ) = 162 N or 36.4 pounds

23 Normal Forces Normal forces, are contact forces that are normal, or perpendicular, to the surface in contact. Say you have a 10 N brick sitting on a table. The Earth pulls down on the brick with a force of 10 newtons. If there was no normal force, the brick would fall through the table. The table exerts a 10 N normal force upon the brick.

24 Normal Forces Example: My weight is 827 N pressing down on the floor. The floor exerts a normal force of 827 N up on me. In general F n = mg cos The magnitude of the normal force is equal to that of the weight when an object is on a horizontal surface. = 0. (cos 0 = 1) F n = mg

25 Normal Forces Normal forces are always perpendicular to the surface, and object is pressed against. F n F n

26 Normal Forces The Red block has mass, m F n = mg cos 0 = mg F n F n = mg cos F n

27 Trig trick F n w F n w F n F n is the adjacent component of the weight

28 Normal Forces Let the mass of the block be 50 kg. F n w = (50 kg)(9.8m/s 2 ) = 490 N F n = (50 kg)(9.8m/s 2 ) cos 30 = 424 N

29 Normal Forces What happens when we increase 90 degrees? F n = (50 kg)(9.8m/s 2 ) cos from 0 to F n = (50 kg)(9.8m/s 2 ) cos 0 = 490 N F n = (50 kg)(9.8m/s 2 ) cos 10 = 483 N F n = (50 kg)(9.8m/s 2 ) cos 30 = 424 N F n = (50 kg)(9.8m/s 2 ) cos 45 = 346 N F n = (50 kg)(9.8m/s 2 ) cos 60 = 245 N F n = (50 kg)(9.8m/s 2 ) cos 90 = 0 N F n

30 Free Body Diagrams A free body diagram is a picture that includes an object, and ALL the forces that are exerted on the object. We will use these a lot because they are very handy. If you set up the diagram correctly, the equations needed for using Newton s 2 nd Law can be visualized.

31 Normal Forces Looking at Newton s 2 nd Law. F = ma A 10 kg book is sitting on a 20 kg desk. What normal force does the ground exert on the desk. B D Free body diagrams F nd F nb w b w b w d

32 Since the book sits still on the desk, a = 0. F = ma = 0, w b + F nb = 0 N. w b = - F nb Also the desk sit still on the ground, a = 0. F = ma = 0, w b + w d + F nb = 0 N. w b + w d = - F nb (remember that forces are vectors) F nb = - m b g = (10 kg)(9.8m/s 2 ) = 98 N upward. F nd = - m b g - m d g = (10 kg +20 kg) )(9.8m/s 2 ) = 294 N upward Notice that to find the normal force the ground exerts on the desk, you use the weight of the book and the desk.

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