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Chapter 3: Newton’s Second Law of Motion

Force and Acceleration

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Galileo Developed the Concept of Acceleration

• Galileo used inclined planes (ramps)

• He found that balls rolling down inclines rolled faster and faster

• Acceleration = change in velocity/ time interval

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Acceleration can be negative

• Example: a car is moving in a certain direction. The driver steps on the accelerator. The car speeds up. The driver lets up on the accelerator and the car starts to slow down. The car decelerated (negative acceleration)

• Deceleration is indicated by an arrow in the opposite direction of motion

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Question: If a car makes a turn, but is going the same speed, is it accelerating?

• Speed doesn’t change, but direction does• Remember that acceleration is change in

velocity/time• Velocity is speed with direction• So, in the scientific sense the car is

accelerating because the car’s direction is changing as it is going around the turn.

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Explanation of Acceleration

• Look at Figure 3.4 on page 36• What would be the reading of the

speedometer at:• Time - 3 sec = ______ m/sec2

• Time - 4 sec = ______ m/sec2

• Time - 5 sec = ______ m/sec2

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Force causes Acceleration

• Acceleration depends on net force. Larger force, larger acceleration and vice versa. Note: with mass constant.

• Example: Suppose you pull a wagon with a net force of 20N. Friction and gravity are working to slow down the wagon - Lets say 10N of force

• The net force on the wagon is 10N and the wagon moves in the direction of the larger force which is the pull that you generated

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Acceleration ~ net force

• ~ stands for directly proportional• As one increases, the other also

increases• As net force increases so does

Acceleration• There is a general rule: if the net force

is X2 then accel. Is doubled• If net force is X3, acel. Is tripled

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Mass of an object corresponds to or relates to inertia

• The greater an object’s mass the greater it’s inertia

• Mass is also a measure of how much material (# and kinds of atoms) an object contains

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Don’t Confuse Mass and Volume

• Volume is the amount of space an object takes up

• Example: 2 bags of equal size (1) contains cotton the other contains rocks

• Equal volumes but not equal masses

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Mass resists Acceleration

• The more massive an object is the more difficult to accelerate it

• Acceleration ~ 1/mass - When Force is constant

• Inverse relationship = mass and acceleration change in opposite ways

• As one goes up the other goes down and vice versa

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Mass resists Acceleration

• The more massive an object the more difficult to accelerate

• Twice as much mass has 1/2 the acceleration

• X3 as much mass results in 1/3 the acceleration

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Newton’s Second Law

• Force = mass x acceleration

• Units• Force = (N)• Mass = kilograms• Acceleration = meters/sec2

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Newton’s 2nd Law

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Friction always acts in a direction to oppose motion

• Friction occurs when one object rubs against something else

• Friction occurs for solids, liquids, and gases

• The amount of friction between two surfaces depends on the kinds of material and how much they are pressed together

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Friction

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Mass vs. Weight

• Mass is the amount of matter in an object

• Weight is the force due to gravity that acts on an objects’ mass

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Mass vs. Weight

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Objects in Free Fall have equal Acceleration

• Gravity - 9.8 m/sec2

• Neglecting air drag or air resistance

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Acceleration is less when air drag acts

• For Free Fall the downward force is weight

• The upward force is air drag (air resistance)

• Net force = weight (N) - air drag (N)

• When air drag = weight we have ∑F = 0

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Does that mean the object in free fall comes to a stop?

• No, the object no longer picks up speed

• Example: Parachutist

• The diver reached terminal speed (velocity)

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Forces on a Parachutist

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