Chapter 6Forces in Motion

Section 1:

Gravity and Motion

Gravity and Motion

• All objects fall with the same acceleration (remember that acceleration is the rate at which velocity changes… Acceleration = Δ v

time)

Objects fall to the ground at the same rate because the acceleration due to gravity is the same for all objects.

Accelerating at a constant rate

• All objects accelerate toward Earth at a rate of 9.8 m/s/s (For every second an object falls, the objects downward velocity increases by 9.8 m/s) regardless of the mass

Velocity of falling objects

• To find the change in velocity (Δ v) of a falling object, multiply the acceleration due to gravity (g or 9.8 m/s/s) by the time it takes that object to fall in seconds.

Δ v = g x t

Let’s look at an example.

Problem 1

A stone at rest is dropped from a cliff, and it takes 3 seconds to hit the ground. Its downward velocity when it hits the ground is?

Δ v = g x t

Δ v = 9.8 m/s x 3s =29.4 m/s

s

Problem 2

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

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

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

9.8 m/s x 2 s = 19.6 m/s s

9.8 m/s x 4.5 s = 44.1 m/s

s

Problem 3

A boy standing on a high cliff dives into the ocean below and strikes the water after 3 seconds. What is the boys velocity when he hits the water?

29.4 m/s downward

Problem 4

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

63.7 m/s downward

Problem 5

A brick falls from the top of a building and strikes the ground with a velocity of 19.5 m/s downward. How long does the brick fall?

2 seconds

Accelerating at a constant rate

Air Resistance Slows down Acceleration

• Fluid friction is also known as air resistance. Air resistance occurs between the surface of falling objects and the air that surrounds it.

Air Resistance Affects Some Objects More Than Others

• The amount of air resistance acting upon an object depends upon the size and shape of the object

Acceleration Stops at the Terminal Velocity

• As an object falls, air resistance continues to increase until it exactly matches the downward force of gravity. The object has then reached its terminal velocity…or a net force of zero

Free fall occurs when there is no air resistance

• Free fall only occurs if there is no gravity pulling it down and no other forces are acting upon it.

Orbiting Objects Are In Free Fall

• Free fall can be either ascending or descending. If you could toss a ball upward with no forces other than gravity acting upon it (no air resistance), its entire path (up and down) would be in free fall.

Two Motions Combine to Cause Orbiting

• An object is orbiting when it is traveling in a circular or nearly circular motion around another object.

• While a space ship orbits the Earth, it is also in free fall toward the Earth. Remember the Space Station example?

How an Orbit is Formed

Why doesn’t the space shuttle fall to Earth if gravity is pulling it downward?

What would happen if the shuttle started moving much faster or much slower?

Projectile Motion and Gravity

• Projectile motion: the curved path an object follows when thrown or propelled near the surface of the Earth.

• Projectile motion has 2 components horizontal and vertical and one has no impact on the other (independent). When combined, they formed a curved path.

Projectile Motion and Gravity

Horizontal Motion

• Horizontal motion is motion parallel to the ground

Vertical Motion

• Vertical motion is motion that is perpendicular to the ground

Chapter 6Forces in Motion

Section 2:

Newton’s Laws of Motion

Newton’s First Law of Motion

• Newton’s first law of motion states that the motion of an object will not change if no unbalanced forces act upon it.

Inertia

• Inertia is the tendency of matter to resist a change in motion.

• Mass is a measure of inertia

Newton’s Second Law

• Newton’s second law of motion states that the acceleration of an object depends on its mass and the force exerted upon it.

Expressing Newton’s Second Law

a= F/ m OR F = m x a OR m = F/a

a = acceleration, m = mass, F = force

Let’s try a few

Second Law Problems

You are hitting an object of unknown mass with a force of 15 N and that object accelerates at 5 m/s/s. What is the mass of the object?

If F = m x a, and 1N = 1kg x m/s/s, then

15 kg x m/s/s = m x 5 m/s/s

3 kg = m

Second Law Problems

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

a = F/m

a = 68.6 N / 7 kg OR a = 68.6 N

7N x m/s/s

a = 9.8 m/s/s

Second Law Problems

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

F = m x a

F = 1,250 kg x 40 m/s/s OR (1,250 N x m/s/s) x 40 m/s/s

F = 50,000 N

Second Law Problems

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

m = F /a

m = 34 N / 4 m/s/s OR (34 kg x m/s/s) / 4 m/s/s

m = 8.5 kg

Complete Math Skills WS

“Newton: Force and Motion”

Newton’s Third Law of Motion

Gravity and Motion

• All objects fall with the same acceleration (remember that acceleration is the rate at which velocity changes… Acceleration = Δ v

time)

Objects fall to the ground at the same rate because the acceleration due to gravity is the same for all objects.

Weird Science

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

Accelerating at a constant rate

• All objects accelerate toward Earth at a rate of 9.8 m/s/s (For every second an object falls, the objects downward velocity increases by 9.8 m/s) regardless of the mass

Velocity of falling objects

• To find the change in velocity (Δ v) of a falling object, multiply the acceleration due to gravity (g or 9.8 m/s/s) by the time it takes that object to fall in seconds.

Δ v = g x t

Let’s look at an example.

Problem 1

A stone at rest is dropped from a cliff, and it takes 3 seconds to hit the ground. Its downward velocity when it hits the ground is?

Δ v = g x t

Δ v = 9.8 m/s x 3s =29.4 m/s

s

Problem 2

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

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

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

9.8 m/s x 2 s = 19.6 m/s s

9.8 m/s x 4.5 s = 44.1 m/s

s

Problem 3

A boy standing on a high cliff dives into the ocean below and strikes the water after 3 seconds. What is the boys velocity when he hits the water?

29.4 m/s downward

Problem 4

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

63.7 m/s downward

Problem 5

A brick falls from the top of a building and strikes the ground with a velocity of 19.5 m/s downward. How long does the brick fall?

2 seconds

Accelerating at a constant rate

Air Resistance Slows down Acceleration

• Fluid friction is also known as air resistance. Air resistance occurs between the surface of falling objects and the air that surrounds it.

Air Resistance Affects Some Objects More Than Others

• The amount of air resistance acting upon an object depends upon the size and shape of the object

Acceleration Stops at the Terminal Velocity

• As an object falls, air resistance continues to increase until it exactly matches the downward force of gravity. The object has then reached its terminal velocity…or a net force of zero

Free fall occurs when there is no air resistance

• Free fall only occurs if there is no gravity pulling it down and no other forces are acting upon it.

Orbiting Objects Are In Free Fall

• Free fall can be either ascending or descending. If you could toss a ball upward with no forces other than gravity acting upon it (no air resistance), its entire path (up and down) would be in free fall.

Two Motions Combine to Cause Orbiting

• An object is orbiting when it is traveling in a circular or nearly circular motion around another object.

• While a space ship orbits the Earth, it is also in free fall toward the Earth. Remember the Space Station example?

How an Orbit is Formed

Why doesn’t the space shuttle fall to Earth if gravity is pulling it downward?

What would happen if the shuttle started moving much faster or much slower?

Projectile Motion and Gravity

• Projectile motion: the curved path an object follows when thrown or propelled near the surface of the Earth.

• Projectile motion has 2 components horizontal and vertical and one has no impact on the other (independent). When combined, they formed a curved path.

Projectile Motion and Gravity

Horizontal Motion

• Horizontal motion is motion parallel to the ground

Vertical Motion

• Vertical motion is motion that is perpendicular to the ground