Chapter 3 Projectile Motion Notes
Introduction
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Nonlinear Motion- Motion along a curved path. e.g. throwing a baseball, cannon, ball rolling off table.
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2 independent “components” of motion: Horizontal = remains constant w/o a force acting on it. Vertical = changes w/ time, g pulls object ↓ at 10m/s/s.
→ Combined effects produce a curved path, however, neither component affects the other. v
Vectors (arrows) help us understand this motion.
3.1 Vector and Scalar Quantities v
Vector quantity: A quantity that requires both magnitude & direction. e.g. velocity, acceleration
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Scalar quantity: A quantity that is described by magnitude only. Can be added, subtracted, multiplied & divided. e.g. mass, volume & time
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Arrows are used to represent vector quantities. length of arrow = magnitude direction of arrow = direction of vector quantity
3.2 Velocity Vectors Follow on the Board Suppose an airplane is flying north at 100km/h and there is a tailwind blowing north at a velocity of 20km/h. v Suppose the same airplane turns around and flies into the wind. v Suppose an airplane flying north at 80km/h caught a strong crosswind of 60km/h blowing west to east. v
3.2 Continued…
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Resultant: the result of adding two vectors. How do you find the resultant? Vectors at right angles: 1. 2. 3.
Draw 2 vectors with tails touching Draw parallel projection of each vector with dashed lines Draw the diagonal (from point where tails are touching)
Vectors not at right angles: 1.
Form a parallelogram, the resultant is its diagonal.
Note: To add 2 vectors that are equal in magnitude & at right angles, we use a square. The diagonal is the square root of 2 or 1.414 times the length of one of its sides.
3.3 Components of Vectors v
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Any vector can be broken down into it’s vertical and horizontal vectors, called components. Resolution: process of determining the components of a vector. (p. 32, Figure 3.7) 1.
Vertical and Horizontal lines are drawn from the tail of the vector.
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A rectangle is drawn that encloses the vector as its diagonal.
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Sides of the rectangle are the desired components.
3.4 Projectile Motion v v
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Projectiles: stone thrown in air, cannon ball, etc. Projectile Motion: →Horizontal velocity remains constant when no horizontal force acts on projectile. → Vertical velocity changes dues to gravity. Combined affect produces curved path, parabola.
3.5 Upwardly Launched Projectiles
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No gravity = projectile follows straight-line path. With gravity = projectile falls beneath line, same vertical distance it would fall from rest. d = ½ gt 2 or d = 5t2
3.5 Continued… v
Figure 3.11, p.36 • • •
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Figure 3.12, p.36 •
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Initial velocity is greater due to increase in angle = higher path
Figure 3.13, p.36 • • •
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Horizontal component is always the same Vertical component changes Resultant = diagonal of rectangle formed
Paths of projectiles with same initial speed but different projection angles. Projectiles reach different height & horizontal distances. Distance is the same for projectiles launched at angles that add up to 90 degrees. Maximum range or distance is obtained at 45 degree angle
If air resistance is small, it will take the same amount of time for projectile to reach its max height as it does to fall For short range projectiles, assume ground is flat. Long range projectiles, account for earth’s curvature.
3.6 Fast-Moving Projectiles-Satellites Earth Satellite: a projectile traveling fast enough to fall around the earth rather than into it. → This speed is 8 km/s or 18,000 mi/h v Satellites orbit above earth’s atmosphere in order to avoid air drag and burning up. →Can’t avoid gravity! v
