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Review 5-7

• 5 Newton’s 3rd Law

• 6 Momentum

• 7 Energy

• Review Questions

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Forces and Interactions

• inter = between

• all forces are interactions between masses

• each mass feels same size force

Newton’s 3rd Law of Motion:

Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.

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5 Newton’s Third Law

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What is the net force on the boxed system? Explain with a diagram.

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What is the net force on the boxed system? Explain with a diagram.

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Force Diagram each object. Which has greater acceleration when

released?

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Vectors• magnitude and direction• represented by arrows• examples: force, velocity, and displacement • vector addition is done tail-to-head• horizontal part is the “x component”• vertical part is the “y component”• Pythagorean theorem applies to x and y

components, i.e.

22 )()( verticalhorizontalSize

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Example: Vector Sum of 1 and 1 is the square root of 2.

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Example: A 30N force + 40N force could be replaced with a single 50N force.

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The x-component of the 50N force is 40N.The y-component of the 50N force is 30N.

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6 Momentum

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Impulse-Momentum

Momentum = mv SI Unit: kg·m/s

impulse = Ft SI Unit: N·s = kg·m/s

• Ft = (mv)

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Conservation of Momentum

• Momentum of a System is constant when the net external force on it is zero.

• This law is usefully applied in many situations

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Conservation of Momentum

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Conservation of Momentum

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Conservation of Momentum

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Bouncing Motion

Dead stop: (mv)= 0 – mv = – mv

Bouncing: (mv) = –mv – mv = – 2mv

• bouncing object exerts/feels twice the impulse as a dead stop

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Collisions

• any brief interaction between masses

• inelastic (heat, sound, etc. are generated)

• elastic (no heat, sound, etc. is created)

• deformation is an important aspect of collisions, e.g. ball being hit by club or bat

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7 Energy

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Work

• W = Fd (F parallel to d)

• W = 0 (F perpendicular to d)

• Work is change in energy

• Energy is the capacity to do work

• Energy can be positional or motional

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Energy

• Positional Energy is called Potential Energy, e.g. stretched spring

• Motional Energy is called Kinetic Energy

• SI Units for Work and Energy:J = Nm = kgm2/s2

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Work-Energy Theorem

• Work = (KE)

• Examples: Positional-Motional

Bow and ArrowMass and SpringInclined PlaneMotor and Car

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Conservation of Energy

• Energy cannot be created or destroyed; it may be transformed (by work) from one form into another, but the total amount of energy never changes.

• Energy Forms include: thermal, elastic, chemical, electromagnetic, nuclear, kinetic.

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Machine

• A device that changes an applied force by increasing it, decreasing it, or changes its direction.

• Examples of Machines: pulley, lever, jack, inclined plane.

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Efficiency

• The percent of the work put into a machine that is converted into useful work output.

efficiency = (work output)/(energy input)

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Review Questions

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1. 100 N,

2. 200 N, or

3. Zero?

In the situation shown the scale reads

What is different here if you held the scale from the right side? If the scale were attached to a wall?

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scale reads 100. Nothing is different.

1. 100 N,

2. 200 N, or

3. Zero?

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1. A.2. B.3. Both the same.

Two identical rubber bands connect masses A and B to a string over a frictionless pulley of negligible mass. The pulley is free and the masses are accelerating.

The amount of stretch is greater in the band that connects

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1. A.2. B.3. Both the same.

pulley is free to turn

does not affect size of interaction between A and B

light frictionless pulley is perfect machine for redirecting a force without changing its size

therefore 3rd Law applies:

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1. A.2. B.3. Both the same.

Two identical rubber bands connect masses A and B to a string over a frictionless pulley of negligible mass.

The pulley is held and the masses are motionless.

The amount of stretch is greater in the band that connects?

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1. A.2. B.3. Both the same.

The pulley is held and the masses are motionless.

The amount of stretch is greater in the band that connects

The string is now interacting individually with each side of the pulley – they are independently hanging and each side holds the entire weight of each object.

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Whenever an interaction occurs in a system, forces occur in equal and opposite pairs. Which of the following do not always occur in equal and opposite pairs?

1. Impulses.2. Accelerations.3. Momentum changes.4. All of these occur in equal and opposite pairs.5. None of these do.

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1. Impulses.2. Accelerations.3. Momentum changes.4. All of these occur in equal and opposite pairs.5. None of these do.

Whenever an interaction occurs in a system, forces occur in equal and opposite pairs. Which of the following do not always occur in equal and opposite pairs?

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In which car will you be moving the fastest at the very bottom of the incline?

1. Front car2. Middle car3. Rear car4. Other

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1. Front car2. Middle car3. Rear car4. Other

In which car will you be moving the fastest at the very bottom of the incline?

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Two smooth tracks of equal length have “bumps”—A up, and B down, both of the same curvature. If two balls start simultaneously with the same initial speed, the ball to complete the journey first is along

1. Track A. 2. Track B. 3. Same

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1. Track A. 2. Track B. 3. Same

Two smooth tracks of equal length have “bumps”—A up, and B down, both of the same curvature. If two balls start simultaneously with the same initial speed, the ball to complete the journey first is along

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Three baseballs are thrown from the top of the cliff along paths A, B, and C. If their initial speeds are the same and air resistance is negligible, the ball that strikes the ground below with the greatest speed will follow path

1. A. 2. B. 3. C. 4. Either A or C.5. All strike with the same speed.

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1. A. 2. B. 3. C. 4. Either A or C.5. All strike with the same speed.

Three baseballs are thrown from the top of the cliff along paths A, B, and C. If their initial speeds are the same and air resistance is negligible, the ball that strikes the ground below with the greatest speed will follow path