K9, K10, K11

Do Now

Objectives K9*, K10, K11AP Physics C: Mechanics

Agenda

1. Review Do Now (5 min)2. Rest of OBJ K9 (20 min)3. OBJ K10 (30 min)4. OBJ K11 (20 min)

K9: Apply the equations of motion involving constant acceleration in one-dimensional motion.

Starting from constant acceleration, ao, we get the equations:

Rather than use calculus all the time, we can just use these general forms.

K9: Apply the equations of motion involving constant acceleration in one-dimensional motion.

Notice that both of these equations are based on time. There are some problems that don’t give a time. By solving one equation for t and substituting it into the other equation, we get a third useful equation:

K9: Apply the equations of motion involving constant acceleration in one-dimensional motion.

“Know these 3 equations or I will eat

you.”

“Nom. Nom. Nom.”

K9: Apply the equations of motion involving constant acceleration in one-dimensional motion.

Example 1:An amateur bowler releases a ball with an initial velocity of 2 m/s; the ball slows down with a constant negative acceleration of -0.2 m/s2. How far does the ball roll before stopping, and how long does it take to stop?

K9: Apply the equations of motion involving constant acceleration in one-dimensional motion.

Example 2:A runner bursts out of the starting blocks 0.1 s after the gun signals the start of the race. She runs at a constant acceleration for the next 1.9 s of the race. If she has gone 8 m after 2.0 s, what are her acceleration and velocity at this time?

K9: Apply the equations of motion involving constant acceleration in one-dimensional motion.

Example 3:On a given flight, a T-38 training jet has an acceleration of 3.6 m/s2 that lasts 5.0 s during the initial phase of takeoff. The afterburners are then turned up to full power for an acceleration of 5.1 m/s2. The speed needed for takeoff is 164 knots (1 m/s = 1.94 knots). Calculate the length of runway needed and the total time of takeoff.

“I have a jet.”

K9 Summary

• Use the kinematic equations to bypass the calculus work when you can.

K10: Apply equations of motion in the context of freely falling objects.

Free Fall: when an object is undergoing gravitational pull towards the earth without interference*.

*Interference includes air resistance (drag), lift, or the ground. =)

K10: Apply equations of motion in the context of freely falling objects.

In free fall, the only force an object experiences is gravity.

We haven’t talked about force yet, but all you need to know is that it causes an acceleration. In this case, the force of gravity causes an acceleration due to gravity, g.

K10: Apply equations of motion in the context of freely falling objects.

In nature, g = 9.81 m/s2

However, on the AP Physics C test, mental math is required, so they use the rounded value of 10 m/s2.

Therefore, in this class, g = 10 m/s2.

K10: Apply equations of motion in the context of freely falling objects.

Warning, common mistake:

Pay attention to the negative sign. Some people get confused if acceleration due to gravity is g or –g. It depends on the coordinate system and how the equation is set up.

K10: Apply equations of motion in the context of freely falling objects.

Let’s look at some examples where the kinematic equations are applied to free fall.

K10: Apply equations of motion in the context of freely falling objects.

Example 1:A person steps off a 3.00 m high diving board and drops into the water below. (a) How long does it take for the person to reach the water and (b) what is the person’s speed upon entering the water?

K10: Apply equations of motion in the context of freely falling objects.

Example 2:You drop a rock from a bridge to the river below. When the rock has fallen 4 m, you drop a second rock. As the rocks continue their free fall, does their separation (a) increase, (b) decrease, or (c) stay the same?

K10: Apply equations of motion in the context of freely falling objects.

Example 3:A volcano shoots out blobs of molten lava, called lava bombs, from its summit. A geologist observing the eruption uses a stopwatch to time the flight of a particular lava bomb that is projected straight upward. If the time for it to rise and fall back to its launch height is 4.75 s, and its acceleration is 10 m/s2 downward, what is the initial speed?

K10: Apply equations of motion in the context of freely falling objects.

Example 4:A hot air balloon is rising straight upward with a constant speed of 6.5 m/s. When the basket of the balloon is 20.0 m above the ground, a bag of sand tied to the basket comes loose. (a) How long is the bag of sand in the air before it hits the ground? (b) What is the greatest height of the bag of sand during its fall to the ground?

K10 Summary

• Use the same equations, but this time g defines your acceleration.

K11: Define and identify inertial and non-inertial reference frames.

We will be learning more about inertia when we start the next unit. However, it is very important that we identify a very interesting property of the universe now.

This property is that of an inertial reference frame.

K11: Define and identify inertial and non-inertial reference frames.

Inertial reference frames are identical, except for a constant adjustment factor.

A quick way to say it is that any experiment done in an inertial reference frame will return identical results as compared to another inertial reference frame.

K11: Define and identify inertial and non-inertial reference frames.

For instance, take an airplane in flight. You take a ball and bounce it. It comes right back up to your hand.

On the ground, another person bounces a ball and it comes right back up to their hand.

What is the only difference between these two reference frames? Velocity.

K11: Define and identify inertial and non-inertial reference frames.

What could the plane do to make the ball not come right back up to your hand?

K11: Define and identify inertial and non-inertial reference frames.

Inertial reference frame: constant velocity.

Non-inertia reference frame: non-constant velocity (acceleration).

K11: Define and identify inertial and non-inertial reference frames.

Examining a train:

K11 Summary

• Inertial: constant velocity.• Non-inertial: acceleration.