Chapter 4 Forces Newton s Laws of Motion

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1 Chapter 4 Forces Newton s Laws of Motion

2 Forces Force A 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) Figure 4.2 shows examples

3 4 Fundamental types of forces Strong nuclear force subatomic particles, hold nucleus together 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. When a force is applied, these laws describe how the velocity responds. Also explains how objects interact when a force is applied by one on another. 1 st Law 2 nd Law 3 rd Law

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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 the 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 my cat ~8 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 Newton s 2 nd Law Book s definition: The acceleration, a, of an object is directly proportional to the net force acting on it and inversely proportionally to its mass.

10 Newton s 2 nd Law Remember that ΣF= ma, is a vector equation. The 2 nd Law is to be applied in the 3 dimensions individually. If there is no net force in a direction, the acceleration is zero, then the velocity in that direction, is constant.

11 Book definition: Newton s 3 rd Law 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. Forces always occur in pairs. Example: If you push on a wall, the wall pushes back onto you.

12 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.

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16 Examples of forces we will work with Gravitational force due to gravity Normal force due to contact Friction forces surfaces sliding against each other Spring forces compressing or stretching a spring Tensions involving ropes, cables, tendons

17 Gravitational force Gravitational force is the mutual attraction between any two objects in the Universe. Determined by: FF gg = GGmm 1mm 2 rr 2 (r is the separation between the two objects.) Gravitation constant G = 6.67 x Nm 2 /kg 2 We will use this more later.

18 Gravitational Force FF gg = GGmm 1mm 2 rr 2 let m 1 equal the mass of the Earth and r the radius of the Earth we get: FF gg = 6.67xx10 11 NNmm 2 /kkkk xx10 24 kkkk mm xx10 6 mm 2 Fg= (9.8 m/s 2 )m 2 = m 2 g Weight w = mg, where g = GM E /r 2

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20 ( lbs)

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22 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 up onto the brick.

23 Normal Forces Example: My weight is 880 N pressing down on the floor. The floor exerts a normal force of 880 N up on me.

24 Normal Forces Normal forces are always perpendicular to the direction of the surface the object is pressed against.

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26 F n is equal to the adjacent (normal) component of the weight. Normal force balances out this component of weight.

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29 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.

30 Book Desk

31 F nd F nd F nb = -m b g F nd = -m b g-m d g = -(10 kg)(-9.8m/s 2 ) = 98 N upward. = -(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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33 Fp

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36 As the angle of inclination increases: F N decreases F P increases As the slope increases, gravity has a greater effect on the object. When incline is vertical, Object resembles falling body F P = weight = mg

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38 Free body diagram F net is the total, or resultant force. It is directed along the plane. Applying the 2 nd Law F net = ma = (50kg)a a = F net /m a = (50kg)g (sin 30)/(50 kg) a = 4.9 m/s 2

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43 First we use the force to find acceleration: a

44 What is the tension in the rope?

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46 Friction Friction is due to surfaces not being perfectly smooth. Friction force ALWAYS opposes the direction of motion. The result of friction forces is energy. (heat) Two types of friction: Static friction force keeps the object at rest, and is needed to be overcome so the object can begin motion. Kinetic friction occurs when one object is sliding against another surface.

47 Friction When is friction used is ordinary life? -car brakes -making a car move forward -driving around a turn -walking - Holding objects together/up -rubbing your hands together to make warmth

48 Friction How to calculate frictional force. Frictional force, F f, depends on the material of the two surfaces involves. Given by coefficient of friction (µ). See table on page 109 for examples. There are two coefficients:

49 See figure 4.21 on page 108.

50 the weight.

51 F s balances out F p From earlier we know F P = mg sin θ When the box is about to slide down: F f = µ s F N = µ s mg cos θ

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57 You hang a mass from a scale. When you jerk the scale upwards, what does the scale read? When you accelerate the scale downward, what does it read? When you jerk the scale upwards, the reading will increase. When you jerk the scale down, the reading decreases.

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62 See example 4.11 Atwood s Machine

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71 A 70 kg person jumps off a 5 meter ledge. Once the person comes in contact with the ground, it takes 0.8 seconds to come to a complete stop. Find the magnitude of the force, the ground exerts on the person during this time. First find the speed that the person hits the ground. Use: vv ff 2 = vv aa xx = gg(5mm) v f = 9.9 m/s

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