# Relative Velocity and Relative Acceleration

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Relative Velocity and Relative Acceleration
The measured speed of an object depends upon the observers reference frame. - The speed of a car measured by an observer standing on the side of the road is different than the speed measured by an observer in another car traveling at a different speed. Example: Two cars are traveling along the highway in the same direction. The first car is traveling at 60 mph. The second car is initially traveling right alongside the first car. How fast is the second car traveling relative to the first car? 0 mph How fast is the second car moving as measured by a stationary radar gun wielding cop? 60 mph If the second car passes the first car and is observed to be traveling at a speed of 20 mph by the first car, what speed would the cop measure for the second car? 80 mph If the two cars were driving towards each other with the second car having a speed of 20 mph greater than the first car, what speed would the first car measure for the second car? 140 mph

Relative motion can most easily be described using vectors
Relative motion can most easily be described using vectors. Relative motion can occur in one, two or three dimensions! Constant velocity of reference frame attached to moving observer. y x y’ x’ B O A Position of B relative to A Position of B relative to origin The position of A with respect to the origin changes in time. Position of A relative to origin We will only consider a constant velocity for the moving observer. The velocity does not have to be constant! We can also look at velocity

CH 4: Forces

How do we cause an object to accelerate?
We can push or pull it in a particular direction. If we push an object that is stationary what happens? The object begins moving in the direction of the push. If we push an object in the same direction it is moving what happens? It begins moving faster in the same direction. If we push an object in the opposite direction it is moving what happens? It begins to slow down, and can eventually begin moving in the opposite direction. If we push on an object in a direction perpendicular to its motion, what happens? The object begins to turn in the direction of the push – changes direction. What do we call the push or pull on an object? Force We can now see that an excess (net) force is required to accelerate an object in a particular direction. An object with no net force undergoes no acceleration. This is called equilibrium. This does not mean that there are no forces acting on the object!!

We can classify forces into two main categories:
Contact Forces Physical contact exists between the object to which the force is being applied. E.g.: Picking up an object, pushing an object Field Forces (Body Forces) No Physical contact – forces act at a distance E.g.: Gravitational forces, electrical forces, magnetic forces Force are vectors with magnitude and direction. You must follow the rules for vectors when using forces! Example: What is the net force for each configuration of forces shown? F1 = 5 N and F2 = 10 N a) b) c) d) a) b) c) d)

Newton’s First Law of Motion
What happens to a book at rest on a table? It continues to remain at rest. What happens to an isolated particle in space that is traveling at a constant velocity? It continues to move at a constant velocity. An object will continue to remain in its current state of motion until some external influence causes its state of motion to change. This is the idea behind Newton’s First Law. Newton’s First Law An object in motion remains in motion and an object at rest remains at rest unless acted upon by an external force. (When viewed from an inertial reference frame.) Inertia An objects state of motion can only be changed by interacting with its environment (force exerted on the object by some external agent). The absence of a force means that the object will not undergo any acceleration, therefore neither the magnitude nor the direction of the objects velocity can be altered. Any object will also resist any changes imposed upon it’s state of motion. Inertia – Resistance to changing an objects state of motion. Inertial Reference Frame – Reference frame that is moving at a constant velocity. Non-Inertial Reference Frame – Reference frame that is accelerating.

What about an object allows it to resist changes to its state of motion?
It’s mass. Mass – Amount of material that makes up an object – How much resistance an object has to a change in motion. Mass is not the same as weight!! – Do not confuse the two. - They are often used interchangeably which is incorrect, especially if you are far from the surface of the Earth. Newton’s Second Law of Motion In order to change the state of motion of an object, the object must undergo an acceleration. This requires the application of an external force to an object of specified mass. Newton’s Second Law F – Sum of the forces – Net force [N = kg m/s2] or [lb] m – Mass [kg] or [Slugs] a – Acceleration [m/s2] or [ft/sec2] The net force applied to a mass will cause that mass to accelerate. An acceleration does not cause a force!

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