Newton’s 2nd LawForce and Acceleration

Ch. 5.1-5.3

Let’s Review:Acceleration

• Who remembers what acceleration is?

• The rate at which velocity is changing

• Is this an increase or decrease in speed?– Both!

• What else can change acceleration?– Change in direction

• Acceleration = CHANGE in velocity/change in time

Objectives

1. Relationship between acceleration and net force

2. Relationship between acceleration and mass

3. Explain Newton’s 2nd Law of Motion

Acceleration

• Force causes acceleration• Acceleration is proportional

to net force• a F• “” doesn NOT mean =• What does “proportional”

mean?

Acceleration• Let’s take a look at the

air track again…

Acceleration

• Formula One car traveling at constant speed of 185mph in a straight line. What is the acceleration?

• Blue-Footed Booby standing on a rock. What is the acceleration?

• In both cases a = 0

Zero Acceleration

• Zero acceleration applies both to the state of rest and constant velocity.

• No change in state of motion. Why?

• Forces that are acting on it are balanced– There’s exactly enough friction

to counteract the force --> . . .

• Zero net force means zero acceleration!

• Zero acceleration is the evidence of zero net force.

Net Force

• Roll ball across floor– Assume that velocity is constant

• What is the net force here?• 0 N! If no acceleration, then no net force.• Suppose I pushed the ball with a force of 5 N. What

would the friction be if the ball maintains a constant velocity?

• 5 N (in the opposite direction of ball) • 5 N of force and 5 N of friction cancel each out and

you have constant velocity.

Mass and Acceleration• Mass resists acceleration• Student/chair demo• Toy car-rubber band demo• More mass --> less acceleration• The same force applied to twice

as much mass results in only 1/2 the acceleration

• For 3 times the mass, only 1/3 the acceleration results

• Acceleration is inversely proportional to mass– Mass increases --> acceleration

decreases

• Acceleration = 1/mass• Values change in opposite

directions (plug in #’s)

Check Question• Suppose the pilot announces that the plane is

flying at a constant 900 km/h and the thrust of the engines is a constant 80,000 N. What is the acceleration of the airplane?

• Zero, b/c velocity is constant• What is the combined force of air resistance that

acts on the plane’s outside surface?• 80,000 N, to produce a zero net force. If

resistance were less, the plane would speed up; if it were more, the plane would slow down.

thrust drag

lift

weight

80,000 N 80,000 N

The acceleration is constant!

LET’S DO WORKSHEET

5-1. FIRST SIDE ONLY.

Nonaccelerated Motion• I’m going to pull a mass across table at a constant

velocity (volunteer to read Newton scale)• What is the acceleration?

– 0, no change in velocity once the mass is moving steadily

• What is the applied force?• What is the value of the net force acting on the

mass?– 0, as evident by the non-changing velocity

Nonaccelerated Motion continued

• There are people out there who can look at this demo and tell me how much friction is acting on this object, as long as there is no acceleration. Are you sitting next to one of those people?

• This is zero net force on a moving system– Zero acceleration applies to state of rest and state of

constant velocity

• The forces acting on the book balance to zero

• Zero acceleration is evidence of zero net force

Newton’s Discovery(This is going to take some brain power…)

• Galileo discovered that two objects will fall at the same time– Drop a book and a pen– But he didn’t know why…

• Newton put it all together• One of the most powerful

laws in physics!• I’m going to try and

explain the relationship between force, mass, and acceleration. (2 kids)

• More on this later with free fall…

Newton’s 2nd Law• If you place force on an object, it will accelerate in the

direction you push it– It accelerates in the direction you push it

• Acceleration is directly proportional to force– If you push it twice as hard, it accelerates twice as much

• Acceleration is inversely proportional to the mass of an object– If it gets twice the mass, it accelerates half as much

• acceleration = force/mass,– a = f/m

• Force = (mass)(acceleration)– F = ma

Your experience

• Take a minute to think of a situation you have had that illustrates Newton’s second law of motion and write it down. Then share it with your neighbor . . .

Newton’s 2nd Law• a = f/m

• What do we notice about this equation?– Plug in the number 5kg for

mass and 10N for force

– Now plug in 20N for force. What happens to acceleration?

• Doubling the net force, doubles the acceleration (show)

• Doubling the mass, halves the acceleration

• Pushing an elephant– cd-rom (Hewitt)

Practice Problems

• For our purposes, let’s always use the equation, F = ma, and sub numbers into parts of the equation.

• Remember– F is always in Newtons– m is always in grams– a is always m/s2

• Let's practice