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### Newton’s Laws

The Study of Dynamics

Isaac Newton

- Arguably the greatest physical genius ever.
- Came up with 3 Laws of Motion to explain the observations and analyses of Galileo and Johannes Kepler.
- Invented Calculus.
- Published his Laws in 1687 in the book Mathematical Principles of Natural Philosophy.

What is Force?

- A force is a push or pull on an object.
- Forces cause an object to accelerate…
- To speed up
- To slow down
- To change direction

Newton’s First Law

- The Law of Inertia.
- A body in motion stays in motion at constant velocity and a body at rest stays at rest unless acted upon by an external force.
- This law is commonly applied to the horizontal component of velocity, which is assumed not to change during the flight of a projectile.

The First Law is Counterintuitive

Aristotle firmly believed this.

But Physics B students know better!

Newton’s Second Law

- A body accelerates when acted upon by a net external force.
- The acceleration is proportional to the net force and is in the direction which the net force acts.
- This law is commonly applied to the vertical component of velocity.

Newton’s Second Law

- ∑F = ma
- where ∑F is the net force measured in Newtons (N)
- m is mass (kg)
- a is acceleration (m/s2)

Units of force

- Newton (SI system)
- 1 N = 1 kg m /s2

- 1 N is the force required to accelerate a 1 kg mass at a rate of 1 m/s2
- Pound (British system)
- 1 lb = 1 slug ft /s2

Newton’s Third Law

- For every action there exists an equal and opposite reaction.
- If A exerts a force F on B, then B exerts a force of -F on A.

FL

FM

20 kg

Working a Newton’s 2nd Law Problem

Step 1:Draw the problemLarry pushes a 20 kg block on a frictionless floor at a 45o angle below the horizontal with a force of 150 N while Moe pulls the same block horizontally with a force of 120 N. What is acceleration?

N

FM

FL

FM

20 kg

FL

FG

FG

Working a Newton’s 2nd Law Problem

Step 2:Diagram- Force diagram

- Free Body diagram

Working a Newton’s 2nd Law Problem

Step 3:Set up equations- F = ma
- Fx = max
- Fy = may

Always resolve two-dimensional problems into two one-dimensional problems.

Working a Newton’s 2nd Law Problem

Step 4:Substitute- Make a list of givens from the word problem.
- Substitute in what you know.

Working a Newton’s 2nd Law Problem

Step 5:Solve- Plug-n-chug.
- Calculate your unknowns.
- Sometimes you’ll need to do kimematic calculations following the Newton’s 2nd law calculations.

Gravity as an accelerating force

A very commonly used accelerating force is gravity. Here is gravity in action. The acceleration is g.

Gravity as an accelerating force

In the absence of air resistance, gravity acts upon all objects by causing the same acceleration…g.

Gravity as an accelerating force

The pulley lets us use gravity as our accelerating force… but a lot slower than free fall. Acceleration here is a lot lower than g.

FL

FM

20 kg

FG

2-Dimensional problemLarry pushes a 20 kg block on a frictionless floor at a 45o angle below the horizontal with a force of 150 N while Moe pulls the same block horizontally with a force of 120 N.

a) What is the acceleration?

b) What is the normal force?

The problem of weight

Are weight and mass the same thing?

- No. Weight can be defined as the force due to gravitation attraction.
- W = mg

mgsin

mgcos

mg

Ramps – 2 DThe normal force is perpendicular to angled ramps as well. It’s always equal to the component of weight perpendicular to the surface.

N = mgcos

mgsin

mgcos

mg

Ramps – 2 DHow long will it take a 1.0 kg block to slide down a frictionless 20 m long ramp that is at a 15o angle with the horizontal?

N = mgcos

V > 0

A > 0

V = 0

A = 0

V > 0

A = 0

V > 0

A < 0

Heavy feeling

Normal feeling

Normal feeling

Light feeling

N

N

N

N

mg

mg

mg

mg

Between

floors

Ground

floor

Just

starting up

Arriving at

top floor

Elevator Ride – going up!V < 0

A > 0

V = 0

A = 0

V < 0

A = 0

V < 0

A < 0

Heavy feeling

Normal feeling

Normal feeling

Light feeling

N

N

N

N

mg

mg

mg

mg

Between

floors

Top

floor

Arriving at

Ground floor

Beginning

descent

Elevator Ride – going down!Friction

- The force that opposes a sliding motion.
- Enables us to walk, drive a car, etc.
- Due to microscopic irregularities in even the smoothest of surfaces.

There are two types of friction Kinetic friction In general fk <= fs

Static friction

- exists before sliding occurs

- exists after sliding occurs

Friction and the Normal Force

- The frictional force which exists between two surfaces is directly proportional to the normal force.
- That’s why friction on a sloping surface is less than friction on a flat surface.

Static Friction

- fssN
- fs : static frictional force (N)
- s: coefficient of static friction
- N: normal force (N)

- Static friction increases as the force trying to push an object increases… up to a point!

A force diagram illustrating Static Friction

Normal Force

Bigger Applied Force

Bigger Frictional Force

Gravity

A force diagram illustrating Static Friction

The forces on the book are now UNBALANCED!

Normal Force

Frictional Force

Even Bigger Applied Force

Gravity

Static friction cannot get any larger, and can no longer completely oppose the applied force.

Kinetic Friction

- fk=kN
- fk : kinetic frictional force (N)
- k: coefficient of kinetic friction
- N: normal force (N)

- Kinetic friction (sliding friction) is generally less than static friction (motionless friction) for most surfaces.

Determination of the Coefficients of Friction

Coefficient of Static Friction

- Set a block of one material on an incline plane made of the other material.
- Slowly increase angle of plane until the block just begins to move. Record this angle.
- Calculate s = tan.

Determination of the Coefficients of Friction

Coefficient of Kinetic Friction

- Set a block of one material on an incline plane made of the other material.
- Slowly increase angle of plane until the block just begins to move at constant speed after giving it a slight tap. Record this angle.
- Calculate k = tan.

Pulley problem

Mass 1 (10 kg) rests on a frictionless table connected by a string to Mass 2 (5 kg). Find (a) the acceleration of each block and, (b) the tension in the connecting string.

m1

m2

Pulley problem

Mass 1 (10 kg) rests on a table connected by a string to Mass 2 (5 kg) as shown. What must the minimum coefficient of static friction be to keep Mass 1 from slipping?

m1

m2

Pulley problem

Mass 1 (10 kg) rests on a table connected by a string to Mass 2 (5 kg). If ms = 0.3 and mk = 0.2, what is a) the acceleration and b) the tension in the string?

m1

m2

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