Finding the Change in VelocityFinding the Change in Velocity

^v = g x t^v = g x t The velocity of falling objectsThe velocity of falling objects To find the change in velocity, multiply the To find the change in velocity, multiply the

acceleration due to gravity (g) by the time acceleration due to gravity (g) by the time it takes for the object to fall in seconds (t):it takes for the object to fall in seconds (t):

For example:For example:

A stone is dropped from a cliff, and it takes A stone is dropped from a cliff, and it takes 3 seconds to hit the ground. Its downward 3 seconds to hit the ground. Its downward velocity when it hits the ground is as velocity when it hits the ground is as follows:follows:

^v = 9.8 m/s / s x 3 s ( the seconds cancel ^v = 9.8 m/s / s x 3 s ( the seconds cancel each othereach other =29.4 m/s=29.4 m/s

Now it’s your turnNow it’s your turn

A penny at rest is dropped from the top of A penny at rest is dropped from the top of a tall stairwell.a tall stairwell.

What is the penny’s velocity after it has What is the penny’s velocity after it has fallen for 2 seconds?fallen for 2 seconds?

The penny hits the ground in 4.5 seconds. The penny hits the ground in 4.5 seconds. What is its final velocity?What is its final velocity?

You should have gotten…You should have gotten…

1. 9.8 m/s / s x 2 s = 19.6 m/s1. 9.8 m/s / s x 2 s = 19.6 m/s 9.8 m/s / s x 4.5 s = 44.1 m/s9.8 m/s / s x 4.5 s = 44.1 m/s

Try it again…Try it again…

1. A boy standing on a high cliff dives into the 1. A boy standing on a high cliff dives into the ocean below and strikes the water after 3 ocean below and strikes the water after 3 seconds.seconds.

What is the boy’s velocity when he hits the water?What is the boy’s velocity when he hits the water?

2. A rock falls from a high cliff and hits the ground 2. A rock falls from a high cliff and hits the ground in 6.5 seconds. What is its final velocity?in 6.5 seconds. What is its final velocity?

3. A brick falls from the top of a building and 3. A brick falls from the top of a building and strikes the ground with a velocity of 19.6 m/s strikes the ground with a velocity of 19.6 m/s How long does the brick fall?How long does the brick fall?

Did you get…Did you get…

1. 29.4 m/s1. 29.4 m/s 2. 63.7 m/s2. 63.7 m/s 3. 2 seconds3. 2 seconds

Is That a Fact!!!Is That a Fact!!!

Air resistence is a result of the fluid friction Air resistence is a result of the fluid friction between the falling object and the air and between the falling object and the air and also the inertia of the particles have to “ also the inertia of the particles have to “ move out of the way” of the falling object.move out of the way” of the falling object.

Because the particles have mass, they Because the particles have mass, they also have inertia that resists movement.also have inertia that resists movement.

Weird ScienceWeird Science

If a penny fell from the top of the empire If a penny fell from the top of the empire state Building ( about 385 m), it would be state Building ( about 385 m), it would be traveling with enough velocity to dent traveling with enough velocity to dent almost anything it struck at ground level.almost anything it struck at ground level.

Newton’s second law of motion and Newton’s second law of motion and mathematical problemsmathematical problems

How to find acceleration:How to find acceleration: a= F/ ma= F/ m the relationship of acceleration (a) to mass the relationship of acceleration (a) to mass

(m) and force (F) can be expressed (m) and force (F) can be expressed mathematically with the above equation.mathematically with the above equation.

It can be rearranged to the following form:It can be rearranged to the following form: F= m x aF= m x a

Both forms of the equation can be used to Both forms of the equation can be used to solve problems. solve problems.

Newton’s second law explains why objects Newton’s second law explains why objects fall to Earth with the same acceleration.fall to Earth with the same acceleration.

For example:For example:The apple and the watermelonThe apple and the watermelon

An apple has less mass, so the gravitional An apple has less mass, so the gravitional force on it is smaller. However, the apple force on it is smaller. However, the apple also has less inertia and is easier to move.also has less inertia and is easier to move.

The watermelon has more mass and The watermelon has more mass and therefore more inertia, so it s harder to therefore more inertia, so it s harder to move.move.

See the problem for the apple..See the problem for the apple..

M=0.102 kgM=0.102 kg F = 1 NF = 1 N 1 N = 1 kg. m/s/s1 N = 1 kg. m/s/s a = 1 kg . m/s/s / 0.102 kg = 9.8 m/s/sa = 1 kg . m/s/s / 0.102 kg = 9.8 m/s/s

See the problem for the See the problem for the watermelon…..watermelon…..

M = 1.02 kgM = 1.02 kg F= 10 NF= 10 N 10 N = 10 kg. m/s/s10 N = 10 kg. m/s/s

a= 10 kg. m/s/s / 1.02 kg = 9.8 m/s/sa= 10 kg. m/s/s / 1.02 kg = 9.8 m/s/s

The answers are the same proving that they fall The answers are the same proving that they fall at the same rate!at the same rate!

Try these…Try these…

1. What is the acceleration of 7 kg mass if 1. What is the acceleration of 7 kg mass if a force of 68.6 N is used to move it toward a force of 68.6 N is used to move it toward the Earth? ( Hint: 1 N is equal to 1 kg . the Earth? ( Hint: 1 N is equal to 1 kg . m/s/s)m/s/s)

What force is necessary to accerelate a What force is necessary to accerelate a 1,250 kg car at a rate of 40 m/s/s?1,250 kg car at a rate of 40 m/s/s?

What is the mass of an object if a force of What is the mass of an object if a force of 34 N produces an acceleration of 4 m/s/s?34 N produces an acceleration of 4 m/s/s?

Did you get….Did you get….

1. a= F/ m= 68.6 N / 7 kg = 9.8 m/s/s 1. a= F/ m= 68.6 N / 7 kg = 9.8 m/s/s (This is acceleration due to gravity.)(This is acceleration due to gravity.) 2. F = m x a = 1,250 kg x 40 m/s/s = 2. F = m x a = 1,250 kg x 40 m/s/s =

50,000 N50,000 N 3. m = F/ a = 34 N / 4 m/s/s = 8.5 kg3. m = F/ a = 34 N / 4 m/s/s = 8.5 kg

Now try theseNow try these

Calculate the force of gravity acting on Calculate the force of gravity acting on your 6 kg backpack. (this is the weight of your 6 kg backpack. (this is the weight of your backpack.) your backpack.)

A 50 kg skater pushes off from the wall A 50 kg skater pushes off from the wall with a force of 200 N. What is the skater’s with a force of 200 N. What is the skater’s acceleration?acceleration?

Answers….Answers….

1. F= 6 kg x 9.8 m/s/s = 58.8 N1. F= 6 kg x 9.8 m/s/s = 58.8 N 2. 4 m/s/s2. 4 m/s/s

Work and PowerWork and Power

Work occurs when force causes an object Work occurs when force causes an object to move in the direction of the force.to move in the direction of the force.

W = F x dW = F x d The answer would be called a Joule (J)The answer would be called a Joule (J) Force is expressed in Newtons (N)Force is expressed in Newtons (N)

Working It OutWorking It Out

Use the equation for work shown to solve the Use the equation for work shown to solve the following problem:following problem:

1.1. A man applies a force of 500 N to push a truck A man applies a force of 500 N to push a truck 100 m ( meters) down the street. How much 100 m ( meters) down the street. How much work does he do?work does he do?

W= F x dW= F x dW =500 N x 100 mW =500 N x 100 mW = 50,000 N*mW = 50,000 N*mW= 50,000 J W= 50,000 J

Now you try….Now you try….

2. A man lifts a barbell using 80 Newtons of 2. A man lifts a barbell using 80 Newtons of force a total distance of 1 meter. How force a total distance of 1 meter. How much work is being done by the man?much work is being done by the man?

The answer….The answer….

W= 80 N x 1 mW= 80 N x 1 m

W= 80 JW= 80 J

3. You have 160 N and 1 m, what is the 3. You have 160 N and 1 m, what is the amount of work?amount of work?

4. You have 80 N and 2 m, what is the 4. You have 80 N and 2 m, what is the amount of work being done?amount of work being done?

5. In which situation do you do more work?5. In which situation do you do more work?

a.a. You lift a 75 N bowling ball 2 m off the You lift a 75 N bowling ball 2 m off the floor.floor.

b.b. You lift two 50 N bowling balls 1 m off the You lift two 50 N bowling balls 1 m off the floor.floor.

The answers…..The answers…..

3. 160 J3. 160 J

4. 160 J4. 160 J

5. Lifting the 75 N ball a distance of 2 m5. Lifting the 75 N ball a distance of 2 m

( 150 J)( 150 J)

PowerPower

Power is the rate at which work is done.Power is the rate at which work is done. To calculate power (P), you divide the To calculate power (P), you divide the

amount of work done (W) by the time (t) it amount of work done (W) by the time (t) it takes to do that worktakes to do that work

P = W/t can also be P = J/t …same thingP = W/t can also be P = J/t …same thingThe first one is the one we will use.The first one is the one we will use.The unit to express power is Joules per The unit to express power is Joules per

second (J/s), which is more simply called second (J/s), which is more simply called watt (W).watt (W).

If you do 50 J of work in 5 seconds, your If you do 50 J of work in 5 seconds, your power is 10 J/s, or 10 W.power is 10 J/s, or 10 W.

Try this:Try this:

You do 100 J of work in 10 seconds, what is You do 100 J of work in 10 seconds, what is your power?your power?

10 J/s10 J/s

Mechanical AdvantageMechanical Advantage

Mechanical advantage= output force/input Mechanical advantage= output force/input forceforce

MA= 500 N / 50 N = 10 NMA= 500 N / 50 N = 10 N

1. You apply 200 N to a machine, and the 1. You apply 200 N to a machine, and the machine applies 2,000 N to an object. machine applies 2,000 N to an object. What is the mechanical advantage? (10 N)What is the mechanical advantage? (10 N)

Mechanical EfficiencyMechanical Efficiency

ME = work output/work input x 100ME = work output/work input x 100

The 100 in this equation means that you are The 100 in this equation means that you are expressing this in percentage.expressing this in percentage.

For example:For example:

500N ( output) / 50 N ( input) (= 10) x 100500N ( output) / 50 N ( input) (= 10) x 100

ME= 1,000 %ME= 1,000 %