PHYSICS 149: Lecture 3 • Chapter 2

– 2.1 Forces – 2.2 Net Force – 2.3 Newton’s first law

Lecture 3 Purdue University, Physics 149 1 Forces • Forces are interactions between objects • Different type of forces: – Contact vs. non-contact forces – Contact forces are due to EM interactions • Forces always exist in pairs – When you push on the ground to walk, the ground pushes back on your foot • Measuring forces: Hooke’s law F = kx • Forces are vectors: magnitude plus direction

Lecture 3 Purdue University, Physics 149 2 Force • Force: a push or pull that one object exerts on another – Force can also be defined as any action that alters a body’s state of rest or of constant speed motion in a straight line. • Forces always exist in pairs – Anything that exerts a force also has a force exerted on it. – For example, when you push on the ground to walk, the ground pushes back on your foot. • Two types of forces on macroscopic objects: – Long-range forces: Forces that do not require the two objects to be touching. Example:) gravity and electromagnetic forces. – Contact forces: Forces that exist only as long as the objects are touching one another. Example: kicking a ball.

Lecture 3 Purdue University, Physics 149 3 How to Measure a Force?

• The SI unit for force is the Newton (N). • One way to measure forces is using springs (F ∝ x). • Hooke’s low for an ideal spring: • F = kx where k is the spring constant

Lecture 3 Purdue University, Physics 149 4 Net Force • More than one force can act on an object at once. • The “net” force means the “total force”. • Be careful since the force is a vector. • The sum is easy if all forces act in the same direction.

• If Fnet = 0 we have “translational equilibrium”.

Lecture 3 Purdue University, Physics 149 5 Adding Vectors in 1-D

• If two vectors are in the same direction, their sum is in the same direction and its magnitude is the sum for the magnitudes of the two. • If two vectors are in opposite directions, the magnitude of their sum is the difference between the magnitudes of the two vectors, and the direction of the vector sum is the direction of the larger of the two.

Lecture 3 Purdue University, Physics 149 6 Forces

Lecture 3 Purdue University, Physics 149 7 Forces

• Quantifies the “interaction” between two objects • 4 Fundamental Forces – Gravity – Electromagnetic – Strong Nuclear – Weak Nuclear

• Forces come in pairs, equal and opposite • Vector – Has magnitude and direction – Be careful when you add two forces!

Lecture 3 Purdue University, Physics 149 8 Contact/Action-at-a-Distance

F F

F

Lecture 3 Purdue University, Physics 149 9 ILQ 1

Which of these is not a long-range force? A) The force that makes lightning flow between an electrically charged cloud and an oppositely charged area on the ground B) The force that keeps the Moon in its orbital path around the Earth C) The force that a person exerts on a chair while sitting D) The force that makes the compass point North

Lecture 3 Purdue University, Physics 149 10 Isaac Newton (1643-1727)

• Newton’s Law of Motion • The law of universal gravitation • Principia

• Newton’s laws form the basis of classical mechanics.

The Principia or Philosophiae naturalis principia mathematica published 1687 Lecture 3 Purdue University, Physics 149 11 Newton’s Laws of Motion

1. An object at rest remains at rest and an object in motion remains in motion unless acted upon by an unbalanced force (law of Inertia) 2. An unbalanced force is equal to the rate of change of momentum ( F = ma ) 3. For every action, there is an equal and opposite reaction. Isaac Newton (1643-1727)

Humans could explain/understand the most complex phenomena with only 3 assumptions.

Lecture 3 Purdue University, Physics 149 12 Newton’s Laws

1. No forces → no change in velocity magnitude or direction

2.

3. For TWO objects, forces on each other are equal and opposite

Lecture 3 Purdue University, Physics 149 13 Newton’s Laws of Motion

1. If the sum of all external forces on an object is zero, then its speed and direction will not change. Inertia 2. If a nonzero net force is applied to an object its motion will change. F = ma 3. In an interaction between two objects, the forces that each exerts on the other are equal in magnitude and opposite in direction.

Lecture 3 Purdue University, Physics 149 14 Newton’s First Law of Motion • An object’s velocity (a vector) does not change if and only if the net force acting on the object is zero. • In other words, if there is no net force on an object, its speed and direction of motion do not change (including if it is at rest). • Also called “the law of inertia.” Inertia means resistance to changes in velocity. – Example: the start or stop of a car’s motion, dusts on clothes, a quarter on top of an index card on a cup. – Note that circular motion is NOT a constant motion, that is, net force is not zero. Why?

Lecture 3 Purdue University, Physics 149 15 Newton’s First Law Objects at rest remain at rest and objects in motion remain in motion in a straight line unless acted upon by an external agent

- External agents are called Forces - Forces change the state of motion of an object

A force which causes a standard mass of 1 kg to have an acceleration of 1 m/s2 is, by definition, a force of 1 newton (N)

Lecture 3 Purdue University, Physics 149 16 Newton’s First Law • An object continues in a state of rest or in a state of motion at a constant speed along a straight line, unless compelled to change that state by a net force • The state of rest and constant velocity are “equivalent” • If the object is in a circular trajectory there must be a force • Leads to the definition of inertia: the tendency of an object to remain at rest • Mass and Inertia are measured in kg

Lecture 3 Purdue University, Physics 149 17 Mass

• The mass of an object quantifies the amount of inertia that an object possesses – an intrinsic property of the object • Objects with a lot of inertia (large mass) are harder to change the state of motion of compared to objects with a small amount of inertia (small mass) • The units of mass are grams, kilograms, or slugs

F Small acceleration

F Large acceleration Lecture 3 Purdue University, Physics 149 18 Weight • Weight is the force of gravity on an object with mass • Units of weight are Newtons or Pounds Same mass but Different weight!

r

On earth W=mg where g=9.8 m/s2

Lecture 3 Purdue University, Physics 149 19 Weight

The weight (W) of an object is equal to the magnitude of the gravitational force acting on a body of mass m W = mg Dropping an object causes it to accelerate at free-fall acceleration g

Fg = mg

W = Fg Lecture 3 Purdue University, Physics 149 20 Weight on Earth • Your weight on Earth is the magnitude of Earth’s gravitational force exerted on you (m).

where R is the distance between you and Earth’s center • The weight of an object of mass m “near” Earth’s surface is:

where (g is called the gravitational field strength)

Lecture 3 Purdue University, Physics 149 21 Weight on Other Planets

• The weight of an object of mass m “near” a planet’s surface is:

• For example, gMoon = 1.62 N/kg ≈ 1/6 gEarth. – Let’s say there is a man whose mass is 100 kg. • At the surface of Earth, his mass and weight are 100 kg and

980 N (=m×gEarth), respectively. • At the surface of Moon, his mass and weight are 100 kg and

162 N (=m×gMoon), respectively.

Lecture 3 Purdue University, Physics 149 22 ILQ 2 A parachutist drifts slowly downwards towards the earth with constant speed. Only two forces, P and W, act on the parachutist. Force P is the upwards pull from the parachute and W is the downwards pull from the Earth. A) P and W are equal in size and opposite in direction B) W is larger than P C) P is larger than W

Lecture 3 Purdue University, Physics 149 23 Free Body Diagrams • A simple recipe:

– Simple picture of just object of interest

– Choose coordinate system (x,y)

– Identify all forces acting on object and draw arrow showing direction

Lecture 3 Purdue University, Physics 149 24 Free Body Diagrams

• “Free-body” means your diagram is free of other objects • “The zeroth law”: An object responds only to forces acting on it! • Draw force vectors only for forces exerted by other objects on the object of interest • Put the tail of the vector on the dot that represents the object of interest • Use a symbol for the force that indicates the kind of force. • Use subscripts to indicate the object on which the force is acting (first subscript) and the object that exerted the force (second subscript)

Lecture 3 Purdue University, Physics 149 25 Labeling Forces • Which force are important when you do FBD? • Draw force vectors only for forces exerted by other objects on the object of interest. First index must always be the one representing the object

Lecture 3 Purdue University, Physics 149 26 Labeling Forces F = Force on 2 by 1 F12= Force on 1 by 2 21

Fmf Ffm Fgc Fcg

Fae F F Fea sh hs

Using indices you can recognize easily force linked by third law Lecture 3 Purdue University, Physics 149 27 Book Pushed Across Table

• Book sliding across table y – Choose Object (book) – Label coordinate axis x – Identify All Forces • Hand (to right) Normal • Gravity (down) • Normal (table, up) friction hand • Friction (table, left)

Gravity Physics

Lecture 3 Purdue University, Physics 149 28 Summary • Force • 4 fundamental forces • Newton’s first law • Inertia: mass vs. weight

Lecture 3 Purdue University, Physics 149 29