Chapter 2

Motion

3 Properties of Motion:

• Speed: Change in distance per unit of time. distance/time or v=d/t. The units can be mi/h, km/h, m/s, etc..

• Velocity: Same as speed but direction is specified as well.

• Acceleration: a = v/t = d/t/t = d/t2. Change in speed per unit of time.

Calculating Speed• A car travels 875 miles in 9 hoursThe speed is:d = 875 mit = 9 hr v = d / tv = ? mi/hr v = 875 mi / 9 h = 97 mi/h• A car travels at 75 mi/h for 42 hours. What is the

distance traveled?• The distance is: v=75 mi/h v = d/tt=42 h v x t = dd=? d = v x t d = 75 mi/h x 42 h = 3150 mi

Velocity

• Describes the speed and direction of an object. e.g. 60 mi/h to the west.

60 km/h east 60 km/h northwest

Acceleration

• Rate at which motion is changed. Change in velocity per unit of time.

• Acceleration = change in velocity time elapsed a = v2-v1

t

Calculation Acceleration• A car is moving at 60 km/h. The driver

accelerates to 80 km/h. If it takes 4 seconds to increase the velocity from 60 km/h to 80 km/h, then what is the acceleration?:

v2=80 km/h a=v2-v1

v1=60 km/h tt=4 s a=80 km/h-60 km/h

4 s a= 20 km/h = 5 km/h 4 s s

Calculation of Acceleration• What is the acceleration of a bicycle which goes

from rest to 12 mi/h in 1.3 minutes? a = ? a = v2 – v1 / t v2 = 12 mi/h a = 12 mi/h – 0 mi/h 1.3 min v1 = 0 mi/h a = 12 mi/h t = 1.3 min 1.3 min a = 9.2 mi/h min

Acceleration

• Negative acceleration occurs when you decelerate or apply brakes.

• A change in direction is a change of acceleration, since it is a change in velocity.

Forces• A push or a pull that is capable of changing the

state of motion of an object.• Net force is a sum of all the forces acting on an

object.• Parallel forces are added. The net force is the

sum.• Opposite parallel forces are subtracted. The net

force is the difference of the greater force minus the smaller force.

• Two net forces which aren’t together or opposite give rise to a new net force. You will have a new direction and a new strength.

Forces

• Force strength and direction can be represented by arrows. The arrowhead is in the direction of the force exerted. The length of the arrow is proportional to the strength of the force.

Horizontal Motion on Land

• Forces applied to an object, such as a ball, must counteract resistance forces for the ball to continue to move forward at a given speed.

• Resistance forces are Ffloor and Fair.• The net force is the Force applied minus

the resistance forces: Fnet=Fapplied-Fresistance

A. The ball is rolling to the left with not forces in the direction of motion. The ball slows to a stop because the only forces are in the opposite direction.B. A force is applied to a moving ball by a hand that moves along with the ball. The forces applied equal the sum of the opposing forces, so the ball continues to move with a constant velocity.

Inertia

• The behavior of matter that causes it to persist in its state of motion.

• The tendency of an object to remain in unchanging motion or at rest in the absence of an unbalanced force; e.g. friction, gravity, etc.

• Satellites continue to move through space without additional forces being applied due to lack of resistance.

Falling Objects• Galileo threw a solid iron

ball and a solid wooden ball from the top of the tower of Pisa. Both balls hit the ground at nearly the same time. Therefore, the velocity is the same.

• The velocity of an object does not depend on its weight. The differences are explained by air resistance.

Falling Objects • Objects fall to the floor

when dropped due to the force of gravity.

• In a free fall (no resistance forces) the object should cover a distance proportional to the square of time:

d α t2.• An object should fall 4

times as far in 2 s as in 1 s. (22=4), 9 times as far in 3 s (32=9)

Falling objects

• The velocity of falling objects increases at a constant rate. The change in velocity in a period of time is acceleration, so an object accelerates towards the surface of the earth due to the force of gravity.

Falling Objects• The acceleration is constant for all objects in

free fall. During each second of fall the object gains 9.8 m/s in velocity.

• This gain is the acceleration of the falling object, 9.8 m/s2, or 32 ft/s2. The symbol g is used for this. Thus g= 9.8 m/s2, or 32 ft/s2

• The acceleration of free falling objects varies slightly from place to place on the earth’s surface due to the earth’s spin, shape, and distribution of mass. It is less at the equator, more at the poles.

Newtons Laws of Motion:Newton’s First Law of Motion

• The law of inertia: Similar to Galileo’s. Inertia is the tendency of an object to resist changes in motion.

• The first law: Every object retains its state of rest or its state of uniform straight line motion unless acted upon by an unbalanced force. The net force must be greater than 0.

• An object moving with uniform straight line motion will retain that motion unless a net force causes it to speed up, slow down, or change directions.

Newton’s Laws of MotionSecond Law of Motion

• A change of motion is evidence of the action of a net force. This is the conclusion from Newton’s first law.

• The acceleration of an object is inversely proportional to its mass.

• a=F/m, so F=ma• Newton is the metric unit for force: 1 newton (N) = 1 kg x m s2

Newton’s Laws of MotionSecond Law of Motion

• Newton’s Second Law states that: The acceleration of an object is directly

proportional to the net force acting on it and is inversely proportional to the mass of the object.

Weight and Mass

• Mass=How much an object resists a change in its motion.

• e.g. Moving a car versus a truck, pushing them into motion.

• Masses are measured on a balance by comparing the force of gravity acting on a standard mass compared to the force of gravity acting on an unknown mass.

• Masses have units of grams or lbs/ft/s2

Mass and Weight

• Weight=The force of gravity acting on a mass. It is a force and has units of pounds or newtons.

• F=ma (Force=mass x acceleration)• Weight is a downward force on a falling object: downward force = (mass)(acceleration due to gravity)g = acceleration due to gravity = 9.8 m/s2

weight = (mass)(g)

Mass and Weight

The pound (lb) in the English system is a unit of force or weight, not mass

1 lb = 4.5 kgxm = 4.5 N s2

Mass and weight are proportional on a given place on earth.

Newton’s Laws of Motion:Newton’s Third Law of Motion

• If an object changes its state of motion it is evidence that an unbalanced force has been applied. This is the conclusion from the first and second laws.

• To produce a force a second object is always pushing or pulling on a first object.

• A single force doesn’t exist by itself. There is always a matched and opposite force that occurs at the same time.

Newton’s Laws of Motion:Newton’s Third Law of Motion

• Newton’s third law of motion states that: Whenever two objects interact, the force exerted on one

object is equal in size and opposite in direction to the force exerted on the other object.

• Forces always occur in matched pairs that act in opposite directions and on two different bodies:

• FA due to B = FB due to A

• For every action there is an equal and opposite reaction.• When a person walks he or she exerts force on the

ground and the ground exerts force on the person. Since the earth is so massive the earth will not accelerate but the person will.

Assignments for Chapter 2

• p. 57 Applying Concepts # 1, 3, 4, 5, 6, 7, 8, 9• P. 58 Parallel Exercises Group A # 1, 2, 3, 4, 5,

6, 7, 8, 10

• New Book: p. 61-65 # 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 25, 32, 33, 34, 37, 43

• p. 65 Group A: # 1, 2, 3, 5, 6, 8, 10, 14, 20, 21, 24

Review for Chapter 2• 3 properties of motion• Calculating speed, velocity, acceleration• Negative acceleration• Forces and Resistance• Inertia• Velocity and Acceleration during free fall• Gravitational acceleration• Newton’s 3 laws• Equation for force• Opposing forces