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Newton’s Laws

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Newton’s Laws

The Study of Dynamics

- 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.

- 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

- 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.

Aristotle firmly believed this.

But Physics B students know better!

- 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.

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

- 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

- 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

Larry 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

N

FM

FL

FM

20 kg

FL

FG

FG

Working a Newton’s 2nd Law Problem

- Force diagram

- Free Body diagram

Working a Newton’s 2nd Law Problem

- F = ma
- Fx = max
- Fy = may

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

Working a Newton’s 2nd Law Problem

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

Working a Newton’s 2nd Law Problem

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

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

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

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.

N

FL

FM

20 kg

FG

Larry 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?

Are weight and mass the same thing?

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

N

mg

N = mg for objects resting on horizontal surfaces.

N

mgsin

mgcos

mg

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

N = mgcos

N

mgsin

mgcos

mg

How 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

friction

applied force

weight

normal

N = applied force

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

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

- 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.

Static friction

- exists before sliding occurs

- exists after sliding occurs

- 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.

- 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!

Normal Force

Frictional Force

Applied Force

Gravity

Normal Force

Bigger Applied Force

Bigger Frictional Force

Gravity

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.

- 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.

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.

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.

N

T

mg

T

-x

mg

x

m1

m2

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

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

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