Lecture 7: Chp 6Lecture 7: Chp 6Newton’s Newton’s

Second Law of Second Law of MotionMotion

Acceleration & ForceAcceleration & Force

Newton’s Second Law of MotionNewton’s Second Law of Motion» Newton’s first law says that a Newton’s first law says that a

force is needed to change an force is needed to change an object’s motion.object’s motion.

» What kind of change happens?What kind of change happens?» AccelerationAcceleration!!

» What is acceleration?What is acceleration?» The rate at which The rate at which velocityvelocity changes changes

over over timetime..

34.Force = Mass x Acceleration

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What is acceleration?What is acceleration?Predict whether the following are Predict whether the following are

true or false.true or false.» If you slow down on your bike, you are If you slow down on your bike, you are

accelerating.accelerating.» If you ride your bike at constant speed, If you ride your bike at constant speed,

you cannot accelerate.you cannot accelerate.» Changing the speed and changing the Changing the speed and changing the

direction of your bike are both direction of your bike are both examples of acceleration.examples of acceleration.

Acceleration: going fast???Acceleration: going fast???» This is where it gets tricky… we typically This is where it gets tricky… we typically

think of acceleration as going fast.think of acceleration as going fast.» Remember that a change in Remember that a change in velocityvelocity

could be a change in speed, a change in could be a change in speed, a change in direction, or both.direction, or both.

» So if you are accelerating, it means you So if you are accelerating, it means you are changing speed (going faster or are changing speed (going faster or slower) or direction.slower) or direction.

» A decrease in speed is called A decrease in speed is called decelerationdeceleration..

» If you slow down on your bike, you are If you slow down on your bike, you are accelerating - accelerating - TRUETRUE: any change in : any change in speed is acceleration.speed is acceleration.

» If you ride your bike at constant speed, If you ride your bike at constant speed, you cannot accelerate. - you cannot accelerate. - FALSEFALSE: you : you could be changing direction.could be changing direction.

» Changing the speed and changing the Changing the speed and changing the direction of your bike are both examples direction of your bike are both examples of acceleration. - of acceleration. - TRUETRUE: any change in : any change in velocity (speed or direction or both)velocity (speed or direction or both)

What is acceleration?What is acceleration?

» Think about it this way…Think about it this way…» What happens when you coast down a What happens when you coast down a

long hill on your bike or board?long hill on your bike or board?» At the top of the hill, you move slowly.At the top of the hill, you move slowly.» As you go down the hill, you move faster As you go down the hill, you move faster

& faster - you accelerate!& faster - you accelerate!» If your speed increases by 1 mph each If your speed increases by 1 mph each

second, then your acceleration is 1 mph second, then your acceleration is 1 mph per second.per second.

What is acceleration?What is acceleration?

Example of Example of AccelerationAcceleration

How Velocity How Velocity ChangesChanges

A plane taking offA plane taking off Increase in Increase in speedspeed

A car stopping at a A car stopping at a stop signstop sign

Decrease in Decrease in speedspeed

Driving around a Driving around a cornercorner

Change in Change in directiondirection

35. Eureka:Acceleration I

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Acceleration EquationAcceleration Equation

36. Eureka:Acceleration II

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How do you calculate acceleration?Example #1Example #1: In a summer storm, the wind : In a summer storm, the wind

is blowing with a velocity of 8 m/s north. is blowing with a velocity of 8 m/s north. Suddenly, in 3 seconds, the wind’s Suddenly, in 3 seconds, the wind’s velocity is 23 m/s north. What is the velocity is 23 m/s north. What is the acceleration in the wind?acceleration in the wind?

23 - 8 m/s23 - 8 m/s = = 15 m/s15 m/s

3 s3 s 3 s 3 s 5 m/s/s or 5 m/s/s or 5 m/s5 m/s22 north north

How do you calculate acceleration?

Example #2: Example #2: You are riding your You are riding your bike downhill at a speed of 15 m/s bike downhill at a speed of 15 m/s west. Five seconds later, you find west. Five seconds later, you find yourself traveling 25 m/s west. yourself traveling 25 m/s west. What is your accelerationWhat is your acceleration

25 - 15 m/s25 - 15 m/s = = 10 m/s10 m/s

5 s5 s 5 s 5 s 2 m/s/s or 2 m/s/s or 2 m/s2 m/s22 west west

How do you calculate acceleration?Example #3Example #3: At point A, a runner is jogging at 3 : At point A, a runner is jogging at 3

m/s. Twenty seconds later, at point B on a hill, m/s. Twenty seconds later, at point B on a hill, the jogger’s velocity is now 1 m/s. What is the the jogger’s velocity is now 1 m/s. What is the jogger’s acceleration from point A to point B?jogger’s acceleration from point A to point B?

1 - 3 m/s1 - 3 m/s = = -2 m/s-2 m/s

20 s20 s 20 s 20 s -0.1 m/s/s or -0.1 m/s/s or -0.1 m/s-0.1 m/s22 up up This person is decelerating, or getting slower.This person is decelerating, or getting slower.

Newton’s Second Law of MotionNewton’s Second Law of Motion» The second law says that the The second law says that the

acceleration of an object acceleration of an object produced by a force is directly produced by a force is directly proportional to the magnitude of proportional to the magnitude of the force, the same direction as the force, the same direction as the force, and inversely the force, and inversely proportional to the mass of the proportional to the mass of the object. object.

Newton’s Law #2Newton’s Law #2» Another way to phrase it: force Another way to phrase it: force causescauses acceleration, & acceleration, &

mass mass resistsresists acceleration. acceleration.» As mass or acceleration increases, force As mass or acceleration increases, force increasesincreases..» As mass or acceleration decrease, force As mass or acceleration decrease, force decreasesdecreases..

Dr Skateboard: Newton’s 2nd law

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Newton’s Law #2Newton’s Law #2» What does this mean, really?What does this mean, really?» Picture a trip to Costco.Picture a trip to Costco.» After grabbing a hot dog or piece of pizza, you grab a cart & start shopping.After grabbing a hot dog or piece of pizza, you grab a cart & start shopping.» At first, the cart is nice & light, and fun to drive around & pretend to race people.At first, the cart is nice & light, and fun to drive around & pretend to race people.» By the time you’re done shopping, what does the cart look like?By the time you’re done shopping, what does the cart look like?

» FULL!!!! FULL!!!! » How does it feel to move it?How does it feel to move it?

» HARD!HARD!» It takes It takes MOREMORE force to accelerate force to accelerate MOREMORE mass. mass.

Force = mass x Force = mass x accelerationacceleration

» It takes one hand to push It takes one hand to push the brick.the brick.

» F = m x aF = m x a

» If you apply twice the If you apply twice the force by using two hands, force by using two hands, the acceleration the acceleration increases by two.increases by two.

» 2F = m x 2a2F = m x 2a

» If you have twice the If you have twice the mass, it takes twice the mass, it takes twice the force to move it at the force to move it at the same acceleration.same acceleration.

» 2F = 2m x a2F = 2m x a

» But if you push two bricks But if you push two bricks with the same force, they with the same force, they accelerate half as fast.accelerate half as fast.

» F = 2m x 1/2aF = 2m x 1/2a

Force = mass x Force = mass x accelerationacceleration

Newton’s Law #2 and Newton’s Law #2 and Falling ObjectsFalling Objects

» Remember what you learned about the Remember what you learned about the rate of acceleration for falling objects?rate of acceleration for falling objects?

» All falling objects fall to the Earth with All falling objects fall to the Earth with the same acceleration… 9.8 m/s/s.the same acceleration… 9.8 m/s/s.

» Does more mass make an object fall Does more mass make an object fall faster? faster? » No, the acceleration is No, the acceleration is alwaysalways 9.8 m/s/s.9.8 m/s/s.

» So let’s see how this works…So let’s see how this works…

Newton’s Law #2 and Newton’s Law #2 and Falling ObjectsFalling Objects

» An object is in free fall if it is An object is in free fall if it is accelerating due to the force accelerating due to the force of gravity & no other objects of gravity & no other objects are acting on it.are acting on it.

» A ball dropped off a cliff is in A ball dropped off a cliff is in free fall until it hits the free fall until it hits the ground.ground.

» Objects in free fall accelerate Objects in free fall accelerate at 9.8 m/sat 9.8 m/s22 on Earth. on Earth.

BrainPops

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» Be sure to watch:» 1. Albert Einstein: click here» 2. Einstein’s Theory of Relativity

37. Newton’s 3 Laws Review

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