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ลำดับตอนที่ #4 : [[R.S.]]Physics Test::Chapter.5::7.9.09

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The Summary of Physics for

Chapter 5:: Projectile Motion

 

Chapter.5 :: Projectile Motion  [[Page.68]]

5-1 Vector and Scalar Quantities [[Page.69]]

-          Physicists often sketch doodles and equations to explain idea.

·         Their doodles include arrows, where each arrow represents the magnitude and the direction of a certain quantity.

-          A quantity that requires both magnitude and direction for a complete description is a vector quantity.

·         Vector, acceleration, and momentum are examples of vector quantities.

-          A quantity that is completely described by magnitude only is a scalar quantity.

·         Scalars can be added, subtracted, multiplied, and divided like ordinary numbers.

-          A vector quantity includes both magnitude and direction, but a scalar quantity includes only magnitude.

5-2 Velocity Vectors [[Page.70]]

-          The velocity of something is often the result of combining two or more other velocities.

·         For example, the airplane’s velocity relative to the ground depends on the airplane’s velocity relative to the air and on the wind’s velocity.

-          When combining vectors that are not parallel, vectors become more useful.

·         The resultant of two perpendicular vectors is the diagonal of a rectangle constructed with the two vectors as sides.

·            For example …Suppose the purple line (left one) represent 3-unit and light blue line (down one) represents 4-unit. Both vectors add to produce a resultant vector (which is the diagonal, dark blue line in the middle) of 5 units. (3² + 4² = 5²)

·         122'>122'>Another example is … 122'>When adding a pair of equal-magnitude vectors that are at right angles to each other, we construct a square in between the two vectors .. so, the length of its diagonal is        (root two). Thus, the resultant is        times either of the vectors. (like … if the two equal vectors of magnitude is 15, their resultant would be 122 ร—15=21.2'> ) 

[As you can see .. the diagonal, dark blue line is the resultant of       (square root two)]

5-3 Components of Vectors [[Page.72]]

-          Two vectors at right angles that add up to a given vector are known as the components of the given vector they replace.

-          The process of determining the components of a vector is called resolution.

-          Any vector drawn can be resolved into vertical and horizontal components that are perpendicular.

·     The perpendicular components of a vector are independent of each other

·     As shown in the figure at the left, vectors X and Y are the horizontal and vertical components of a vector V.

 

5-4 Projectile Motion [[Page.73]]

-          A projectile is any object that moves through the air or spaced, acted on only by gravity (and air resistance, if any).

-          Projectiles near the surface of Earth follow a curved path.

-          The horizontal component of motion for a projectile is just like that horizontal motion of a ball rolling freely along a level surface without friction.

·         Rolling ball along a horizontal surface has a constant velocity because no component of gravitational force acts horizontally.

·         The same is also true for a projectile – when no horizontal force acts on the projectile, the horizontal component of velocity remains constant.

-          The vertical component of a projectile’s velocity is like the motion for freely falling object

·         Gravity acts vertically downward. Like a dropping ball, a projectile accelerates downward and its vertical component of velocity changes with time.

·         The increasing speed in the vertical direction causes a greater distance to be covered in each successive equal time interval.

-          Most important, the horizontal component of motion for a projectile is completely independent of the vertical component of motion. Each component is independent of the other. Their combined effects produce variety of curved paths that projectile follow.

5-5 Projectiles Launched Horizontally [[Page.74]]

-          The two important things to notice in the right picture are…

1.       The ball’s horizontal component of motion remains constant. The ball moves the same horizontal distance in the equal time intervals between each flash, because no horizontal component of force is acting on it. (the only acceleration of the ball is downward due to gravity)

2.       The balls fall the same vertical distance in the same time. The vertical distance fallen has nothing to do with the horizontal component of motion.

-          The downward motion of a horizontally launched projectile is same as that of free fall.

-          The path traced by a projectile accelerating only in the vertical direction while moving at constant horizontal velocity is a parabola.

5-6 Projectiles Launched at an Angle [[Page.75]]

-          A projectile’s path is called its trajectory.

-          No matter the angle at which a projectile is launched, the vertical distance of fall beneath the idealized straight-line path (the imaginary path if there were no gravity) is the same for equal time.

a.       The trajectory of the stone combines horizontal motion with the pull of gravity

b.       The trajectory of the stone combines the upward motion with the pull of gravity

c.       The trajectory of the stone combines downward motion with the pull of gravity

The vertical distance is independent of what’s happening horizontally. (Please see the pictures in page 75 of the book .. I can’t find them in the internet sorry T^T)

-          With no gravity, the projectile would follow the straight-line path that keeps on going diagonally upward (dashed line). But because of gravity, the vertical distance it falls beneath any point on the dashed line is the same vertical distance it would fall if it were dropped from rest.

·         This distance is given by 12d= 12gt2'>, where t is the elapsed time. Using the value of 10 m/s² for g in the equation yields d = 5t²

-          The vertical distance a projectile falls below an imaginary straight-line path (dashed line) increases continually with time and is equal to 5t² meters.

·         Notice the figure at the right, the horizontal component is always same and that only the vertical component changes. The actual resultant velocity is represented by the diagonal line formed by the vector components.

ð At the top of the path the vertical component shrinks to zero, so the velocity there is the same as the horizontal component of velocity at all other points. Everywhere else the magnitude of velocity is greater, just as the diagonal of a rectangle is greater than either of its sides. 

-          When the path traced by a projectile has the same launching speed but steeper angle, the initial velocity vector has a greater vertical component than when the projection angle is less. This greater component results in higher path

·         However, since the horizontal component is less, the range is less.

-          Look at the cannon picture at the left, it shows the paths of several projectiles all having the same initial speed but different projection angles. (neglects the air resistance)

·         These projectiles reach different height (attitude) above the ground and also they travel at different horizontal distances, that is, they have different horizontal ranges.

·         The same range is obtained for 2 different projection angles – angles that add up to 90 degrees. (Eg. At an angle of 30 degree, the object fall the same range as if it were thrown at 60 degree with the same speed)

ð The smaller the angle, the shorter time the object remains in the air.

·         Maximum rage ins attained at an angle of 45^o

-          When the effect of air resistance is significant, the range of a projectile is diminished (decreased) and the path is not a true parabola.

·         If air resistance is negligible, a projectile will rise to its maximum height in the same time it takes to fall from the height to the ground due to constant effect of gravity. The deceleration due to gravity going up is the same as the acceleration due to gravity going down. So the projectile hits the ground with the same speed it had originally when it was projected upward from the ground.

·         For short-range projectile motion, we usually assume that ground is flat. However, for very long range projectiles the curvature of Earth’s surface must be taken into account.

 

Ps. Sorry for the mistakes ^__^ ,,

Gdluck in the test na ja 



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