7.1     Momentum

Momentum (Inertia in motion) – The mass of an object multiplied by its velocity.

• momentum (mv) = mass • velocity   (p)
• A moving object can have a large momentum if it’s mass is large or if it’s velocity is large or both.
• Stationary objects have no momentum.

7.2     Impulse Changes Momentum

• Mass, velocity, or both have a direct impact on Momentum. If the momentum of an object changes, either the mass, velocity or both have changed.
• Force produces acceleration.
• The amount of time a force acts on an object is also important.
• Quantity force • time interval = Impulse
• Impulse = F ∆t
• Ft = ∆mv
• Impulse-momentum relationship allows us to analyze multiple situations where momentum changes.

Increasing momentum – apply the greatest force possible for the longest time possible.

• Impact forces = average force of impact.
• Impact refers to a force (N)
• Impulse refers to impact force • time (Ns)

Decreasing momentum – extend the time of impact in order to reduce the force of the impact.

• A difference in impact time is important even if you can’t notice the give in the surface.

7.3     Bouncing

• Impulses are greater when an object bounces.
• More impulse is required to make an object completely stop than for the object to change directions.
• Lester A. Pelton discovered that the flat paddles on waterwheels were inefficient.

Result of a collision – The motion of one or both objects changes drastically during the collision.

• Rather than attempting to understand the details of a collision, we focus on the total change from initial to final conditions.

Lab Simulation

Set up: Have a “frictionless” track on a flat surface with a force detector attached to one end and a motion detector attached to the opposite end. Use one of the cars and attach a spring to the end facing the force detector. Zero the force and position JUST before the spring would contact the force detector.

From the data we concluded:

• Both positive and negative – because the spring compresses a small amount during contact
• There is a force upon contact but not before and after (constant velocity)
• Change in direction, same speed, change in velocity
• Car maintains the same energy

Our model cannot be based on Energy or Speed. It must be based on directional velocity (+ or –). There will be more change if the car starts and bounces back rather than start and stop.

Using our data we came up with the following equations:

From that we established that there is a direct relationship: The higher the impulse, the higher the ∆v. Furthermore, the slope of the graphs (see below) is equal to the mass. From these conclusions we came up with the equation for impulse:

• Impulse = mass • ∆v

8.5     Kinetic Energy

Kinetic Energy (KE) – Energy of motion (motion capable of doing work).

• Kinetic energy = 1/2 mass • speed
• KE = 1/2 mv^2
• KE is equal to the work required to bring the speed from rest.
• net force • distance = kinetic energy
• Fd = 1/2 mv^2

Work-energy theorem – Work = ∆E

8.6     Conservation of Energy

• Understanding how energy transforms is more important than being able to define energy – this is most easily accomplished by analyzing the transformation of one form of energy to another form of energy.
• Energy transforms without net loss or net gain.

Law of conservation of energy – Energy cannot be created or destroyed. It can be transformed from one form to another, but the total amount of energy never changes.

Thermonuclear Fusion – high-temperature welding of atomic nuclei.

• Releases radiant energy – some reaches Earth, other falls on plants (turning some to coal).
• Sun’s energy is used to evaporate water from the ocean – Circle of life and nature.

• The force graph from the ∆Distance and Force Lab has a linear trend line and a direct relationship.
• The energy graph from the ∆Distance and Energy Lab can use either a Power or Polynomial graph, meaning that it is a squared graph.
• From the Distance/Force lab our stiffness constant was 28.95 N/m (after converting from cm) and our coefficient for the Distance/Energy graph was 13.651 N/m (approximately half) which helps prove the following:

• We also determined encountering a constantly increasing force creates the same issue with equatoins that constant acceleration did. Because of this we do not have a simple equation like work = force • distance, we have the more complex equation listed above.

Our Board:

Data:

To begin with, our spring was 22.5cm long. In the “Distance” column we subtracted 22.5cm from the distance that the spring reached after the specified force was applied. We did this to find the “stretchiness” or change in distance so that we were able to record concise data.

Graph:

Conclusions:

• Slope of the graph = “Stretchiness” – For every 1 N, the spring stretches 3.56cm
• The larger the coefficient of the equation of the line on the graph, the more stretched out the spring was to begin with.
• Spring Stiffness is represented by the equation: F = k d + 0     (F = force, k = stiffness, d = distance)

8.1     Work

Work – Quantity (distance) of force x distance.

• Application of a force and the movement of something by the force are componets of every case where work is done.
• Work = f d     (work = force x distance)

Work is measured in one of two ways:

1. Newton-meter (N•m)
2. Joule (J)     [Named after James Joule]

• One joule of work is done when a force of 1 N is applied over a distance of 1 meter.

8.2     Power

Power – The rate at which work is done.

• Power = (work done) / (time interval)

Watt – The power expended when one joule of work is done in one second.

8.3     Mechanical Energy

Energy – “Something” that enables an object to do work.

• Measured in joules

Mechanical Energy – The energy due to the position of something or movement of something.

8.4     Potential Energy

Potential Energy (PE) – Energy that is stored and held in readiness.

• Gravitational Potential Energy = Weight x Height     (PE = mg h)

11.4     Rotational Inertia

Rotational Inertia (Moment of Inertia) – The resistance of an object to changes in its rotational motion.

• Rotating objects keep rotating, stationary objects stay stationary.
• Depends on mass and distribution of the mass.
• Larger distance between the bulk of the mass and the axis of rotation creates a larger rotational inertia.
• I = mr^2     (inertia = mass x rotational axis)

11.5     Rotational Inertia and Gymnastics

• The human body has many axes of symmetry. Rotational inertia differs upon each axis. Rotatioal inertia is about the transverse and median axes.

11.6     Angular Momentum

Linear Momentum – “Inertia of motion” or momentum (mass x velocity).

• Linear momentum = mass x velocity

Angular Momentum – “Inertia of rotation” or rotation of objects.

• Angular Momentum = Rotational inertia x Rotational velocity
• Angular Momentum = I ω
• Angular Momentum = mv r     (magnitude of linear momentum x radial distance)

Rotational Velocity – A direction that is assigned to rotational speed.

• Similarly to linear momentum, angular momentum is a vector quantity (has direction AND magnitude).

11.7     Conservation of Angular Momentum

Law of conservation of angular momentum – If no unbalanced external torque acts on a rotating system, the angular momentum of that system is constant.

• No external torque means the product of rotational inertia and rotational velocity will, at one time, be the same at any other time.

9.1     Rotation and Revolution

Axis – The straight line around which rotation takes place.

Rotation (spin) – When an object turns about an internal axis.

Revolution – When an object turns about an external axis.

9.2     Rotational Speed

Linear Speed – Distance moved per unit of time.

Tangential Speed – The speed of something moving along a circular path.

Rotational Speed – The number of rotations per unit of time.

• Tangential speed ~ radial distance • rotational speed

9.3     Centripetal Force

Centripetal Force – Any force that causes an object fo follow a circular path.

When examining the movements of the ice skater, we concluded that it is not the angular speed that effects her movement, it is the linear speed.

This demonstrates that the right side of the ball is moving further than the left at any given time.

• Air pressure: molecules and oxygen colliding together – they become faster and react with one another.
• If air pressure in a container is less then the atmospheric pressure must be greater in order to allow it to close in on a box (collapse).
• As temperature increases, pressure increases (direct relationship).
• As density decreases, pressure increases (indirect relationship).
• As volume decreases, pressure increases (indirect relationship).
• As speed increases, volume decreases (indirect relationship).
• We don’t “burst” because the pressure inside us equals that of the pressure challenging us.
• When traveling below the surface (in water) the pressure increases at a fairly constant rate.
• Air is considered fluid (generic term for gases and liquids) in terms of Physics.