- Newton's 2nd Law of Motion
- Air Resistance
- Free Fall (straight down)
- Free Fall (thrown straight up)
- Free Fall (projectile/ at an angle)
- Free Fall (thrown up at an angle)
- Air Resistance
NEWTON'S 2ND LAW
Newton's 2nd Law states that acceleration is proportional to force, and inversely proportional to mass. This can be illustrated symbolically like so:
OR they can be combined, creating the equation:
One important concept involved with Newton's 2nd law is the relationship between weight and mass - they are NOT the same thing. If in a problem, you are given the mass and must figure out what the weight is, you can use this conversion equation:
The number (10) is the constant physicists use in place of gravity (g). In labs, to be more precise, use 9.8 as the (g).
FREE FALL - STRAIGHT DOWN
Free fall is when an object falls due to the effect of gravity only. This means no force of air resistance. In real life, an object can only be in free fall when in a sealed vacuum. The equation used for an object free falling straight down is
To find how fast the ball was moving when it hit the ground, you can use the equation:
AIR RESISTANCE
There are two factors that change air resistance: speed and surface area. As speed or surface area increases, so does air resistance, making them directly proportional.
If a person were to jump off a cliff, his force of weight (fweight) is much greater than his force of air resistance (fair). Speed is directly proportional to air resistance. Since all falling objects want to reach equilibrium, the only way for the person to increase his air resistance is to also increase his speed, to reach terminal velocity.
FREE FALL - STRAIGHT UP
How is throwing something up different from dropping?
- When throwing an object up, it has an initial velocity
- This changes our equations (d = 1/2(10)t
²)and(v = gt) because they assume an object starts at rest
²)This only gives us half the parabola, so you must then multiply that amount by 2 to get the total time or distance.
The best way to answer problems involving straight up free fall is by drawing a picture like this:
Note the number of seconds and the velocity of the ball at each second.
FREE FALL - PROJECTILE/ AT AN ANGLE
Projectile throwing is much like free fall straight down, however, one must take the horizontal velocity into account as well as the vertical. Finding horizontal velocity is easier because it stays constant (due to Newton's first law).
If given the distance (d) in the graph shown above, you can use the (d = 1/2(10)t
²) equation to solve for the time (t). Once you know the time, you can use the (v=d/t) equation to find the horizontal velocity.
FREE FALL - THROWN UP AT AN ANGLE
Throwing an object up and at an angle is simply a compilation of the skills we learned from straight up free fall and free fall at an angle
All the problems we are given this year will have an angle of 45 degrees. You can determine the height, distance, horizontal velocity and vertical velocity of the object using skills from the lessons above.
However, to find the diagonal velocity of the ball, you must remember your special right triangles:
(Note: The square root of 2 equals around 1.41, so if you see a measurement of 14.1, 141, 1,410, assume the triangle is this special right triangle)
For example, if you know the horizontal velocity is 30, and the vertical velocity is 40, you can assume the diagonal distance id 50:
