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Chapter 4 The Laws of Motion

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Chapter 4

The Laws of Motion

Sir Isaac Newton

(1643 – 1727)

- Newtonian mechanics
- Describes motion and interaction of objects
- Applicable for speeds much slower than the speed of light
- Applicable on scales much greater than the atomic scale
- Applicable for inertial reference frames – frames that don’t accelerate themselves

- Force
- What is a force?
- Colloquial understanding of a force – a push or a pull
- Forces can have different nature
- Forces are vectors
- Several forces can act on a single object at a time – they will add as vectors

- Force superposition
- Forces applied to the same object are adding as vectors – superposition
- The net force – a vector sum of all the forces applied to the same object

- Newton’s First Law
- If the net force on the body is zero, the body’s acceleration is zero

- Newton’s Second Law
- If the net force on the body is not zero, the body’s acceleration is not zero
- Acceleration of the body is directly proportional to the net force on the body
- The coefficient of proportionality is equal to the mass (the amount of substance) of the object

- Newton’s Second Law
- SI unit of force kg*m/s2 = N (Newton)
- Newton’s Second Law can be applied to all the components separately
- To solve problems with Newton’s Second Law we need to consider a free-body diagram
- If the system consists of more than one body, only external forces acting on the system have to be considered
- Forces acting between the bodies of the system are internal and are not considered

Chapter 4

Problem 12

Two forces are applied to a car in an effort to move it. (a) What is the resultant of these two forces? (b) If the car has a mass of 3 000 kg, what acceleration does it have? Ignore friction.

- Newton’s Third Law
- When two bodies interact with each other, they exert forces on each other
- The forces that interacting bodies exert on each other, are equal in magnitude and opposite in direction

- Forces of different origins
- Gravitational force
- Normal force
- Tension force
- Frictional force (friction)
- Drag force
- Spring force

- Gravity force (a bit of Ch. 7)
- Any two (or more) massive bodies attract each other
- Gravitational force (Newton's law of gravitation)
- Gravitational constant G = 6.67*10 –11 N*m2/kg2 = 6.67*10 –11 m3/(kg*s2) – universal constant

Gravity force at the surface of the Earth

g = 9.8 m/s2

- Gravity force at the surface of the Earth
- The apple is attracted by the Earth
- According to the Newton’s Third Law, the Earth should be attracted by the apple with the force of the same magnitude

- Weight
- Weight (W) of a body is a force that the body exerts on a support as a result of gravity pull from the Earth
- Weight at the surface of the Earth: W = mg
- While the mass of a body is a constant, the weight may change under different circumstances

- Tension force
- A weightless cord (string, rope, etc.) attached to the object can pull the object
- The force of the pull is tension ( T )
- The tension is pointing away from the body

Free-body diagrams

- Normal force
- When the body presses against the surface (support), the surface deforms and pushes on the body with a normal force (n) that is perpendicular to the surface
- The nature of the normal force – reaction of the molecules and atoms to the deformation of material

- Normal force
- The normal force is not always equal to the gravitational force of the object

Free-body diagrams

Free-body diagrams

Chapter 4

Problem 30

An object with mass m1 = 5.00 kg rests on a frictionless horizontal table and is connected to a cable that passes over a pulley and is then fastened to a hanging object with mass m2 = 10.0 kg, as shown in the Figure. Find the acceleration of each object and the tension in the cable.

- Frictional force
- Friction ( f) - resistance to the sliding attempt
- Direction of friction – opposite to the direction of attempted sliding (along the surface)
- The origin of friction – bonding between the sliding surfaces (microscopic cold-welding)

- Static friction and kinetic friction
- Moving an object: static friction vs. kinetic

- Friction coefficient
- Experiments show that friction is related to the magnitude of the normal force
- Coefficient of static frictionμs
- Coefficient of kinetic frictionμk
- Values of the friction coefficients depend on the combination of surfaces in contact and their conditions (experimentally determined)

Free-body diagrams

Free-body diagrams

Chapter 4

Problem 49

Find the acceleration reached by each of the two objects shown in the figure if the coefficient of kinetic friction between the 7.00-kg object and the plane is 0.250.

Answers to the even-numbered problems

Chapter 4

Problem 2

25 N

Answers to the even-numbered problems

Chapter 4

Problem 6

7.4 min

Answers to the even-numbered problems

Chapter 4

Problem 26

4.43 m/s2 up the incline, 53.7 N

- Answers to the even-numbered problems
- Chapter 4
- Problem 40
- 55.2°;
- (b) 167 N

- Answers to the even-numbered problems
- Chapter 4
- Problem 50
- 18.5 N;
- (b) 25.8 N