IB Physics/Mechanics
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Topic 2: Mechanics
Contents |
[edit] Kinematics (2.1)
[edit] Kinematic concepts
2.1.1 Define displacement, velocity, speed and acceleration.
| Symbol | Definition | SI Unit | Vector or Scalar? | |
|---|---|---|---|---|
| Displacement | s | The distance moved in a particular direction | m | Vector |
| Velocity | v or u | The rate of change of displacement. Velocity = change of displacement over time taken | m s-1 | Vector |
| Speed | v or u | The rate of change of distance. Speed = distance gone over time taken | m s-1 | Scalar |
| Acceleration | a | The rate of change of velocity. Acceleration = change of velocity over time taken | m s-2 | Vector |
- Vector quantities always have a direction associated with them.
2.1.2 Define and explain the difference between instantaneous and average values of speed, velocity and acceleration.
- Average value - over a period of time.
- Instantaneous value - at one particular time.
2.1.3 Describe an object's motion from more than one frame of reference.
[edit] Graphical representation of motion
2.1.4 Draw and analyse distance–time graphs, displacement–time graphs, velocity–time graphs and acceleration–time graphs.
2.1.5 Analyse and calculate the slopes of displacement–time graphs and velocity – time graphs, and the areas under velocity–time graphs and acceleration–time graphs. Relate these to the relevant kinematic quantity.
[edit] Uniformly accelerated motion
Determine the velocity and acceleration from simple timing situations
Derive the equations for uniformly accelerated motion.
Describe the vertical motion of an object in a uniform gravitational field.
Describe the effects of air resistance on falling objects.
Solve problems involving uniformly accelerated motion.
[edit] Forces and Dynamics (2.2)
[edit] Forces and free-body diagrams
[edit] Newton’s first law
Newton's First Law of Physics states that in the absence of a resultant force, a body will remain with its state of motion.
[edit] Equilibrium
[edit] Newton’s second law
ΣF = ma
Alternately: ΣF = Δp/Δt In words, the resultant force is all that matters in the second law. The direction of motion depends on the direction of the resultant force.
[edit] Newton’s third law
For every action, there is an equal and opposite reaction.
[edit] Inertial Mass, Gravitational Mass and Weight (2.3)
An object's inertial mass is defined as the ratio of the applied force F, to its acceleration, a.
Inertialmass = F / a
[edit] State Newton's first law of motion (2.2.4)
In ancient times, Aristotle had maintained that a force is what is required to keep a body in motion. The higher the speed, the larger the force needed. Aristotle's idea of force is not unreasonable and is in fact in accordance with experience from everyday life: It does require a force to push a piece of furniture from one corner of a room to another. What Aristotle failed to appreciate is that everyday life is plagued by friction. An object in motion comes to rest because of friction and thus a force is required if it is to keep moving. This force is needed in order to cancel the force of friction that opposes the motion. In an idealized world with no friction, a body that is set into motion does not rquire a force to keep it moving. Galileo, 2000 years after Aristotle, was the first to realize that the state of no mtion and the state of motion with constant speed in a straight line are indistinguishable from each other. Since no force is present in the case of no motion, no forces are required in the case of motion in a straight line with constant speed either. Force is related to changes in velocity (i.e. acceleration)
Newton's first law (generalizing Galileo's statements) states the following:
When no forces act on a body, that body will either remain at rest or continue to move along a straight line at constant speed.
A body that moves with acceleration (i.e. changing speed or changing direction of motion) must have a force acting on it. An ice hockey puck slides on ice with practically no frction and will thus move with constant speed in a straight line. A spacecraft leaving the solar system with its engines off has no force acting on it and will continue to move in a straight line at constant speed (until it encounters another body that will attract or hit it). Using the first law, it is easy to see if a force is acting on a body. For example, the earth rotates around the sun and thus we know at once that a force must be acting on the Earth.
Newton's first law is also called the law of Inertia
Inertia is the reluctance of a body to change is state of motion. Inertia keeps the body in the same state of motion when no forces act on the body. When a car accelerates forward, the passengers are thrown back into their seats. If a car brakes abruptly, the passengers are thrown forward. This implies that a mass tends to stay in the state of motion it was in before the force acted on it. The reaction of a body to a change in its state of motion is inertia.
A well-known example of intertia is that of a magician who very suddenly pulls the tablecloth off a table leaving all the plates, glasses, etc., behind on the table. The inertia of these objects make them 'want' to stay on the table where they are. Similarly, if you pull very suddenly on a roll of kitchen paper you will tear off a sheet. But if you pull gently you will only succeed in making the paper roll rotate.
