Gravity and free fall Pg. 13

Objectives Physics terms Define the conditions for free fall. Describe and analyze the motion of objects in free fall using the equations for constant acceleration. acceleration quadratic equation free fall

Equations V (or Vf)  final velocity V0 (or Vi ) initial velocity a acceleration t time x (or xf) final position x0 (or xi) initial position V0 (or Vi ) initial velocity t time a acceleration

What is free fall? An object is in free fall whenever it moves solely under the influence of gravity, regardless of its direction. A ball thrown up, with negligible air resistance A ball launched at ANY angle, as long as there is negligible air resistance A ball falling down, with negligible air resistance

Gravity and free fall Near Earth’s surface, free-falling objects have a downward acceleration of -9.8 m/s2. If an object is dropped from rest, then . . . after 1 second its velocity is: -9.8 m/s. after 2 seconds its velocity is: -19.6 m/s. after 3 seconds its velocity is: __?___ after 10 seconds its velocity is: __?___ -29.4 m/s -98 m/s

Describe free fall with equations The free fall equations are identical to the equations for motion with constant acceleration: 𝒗= 𝒗 𝟎 + −𝟗.𝟖 𝒕 𝒙= 𝒙 𝟎 + 𝒗 𝟎 𝒕+ 𝟏 𝟐 (−𝟗.𝟖) 𝒕 𝟐 The only difference is that you already know the acceleration because it is always -9.8 m/s2 (as long as you’re on Earth) Point out that the value of g actually depends on location, and will be different on the Moon, for example. It is 9.8 m/s/s for events close to the Earth’s surface.

Find your reaction time Use this equation for free fall to find your own reaction time—the time to catch a falling ruler. Make a prediction first: Will your reaction time be in seconds? Tenths of a second? Hundredths of a second? 𝑡= −2 𝑦 𝑓 𝑎 𝑎=−9.8 𝑚/ 𝑠 2 Students should complete the student assignment sheet while doing this experiment.

Find your reaction time, treaction Solve for treaction. What is xi? What is vi? What is a? 𝑡= −2 𝑦 𝑓 𝑎 Be aware that many if not most students will forget to convert the free fall distance x from centimeters into meters, and will be baffled at the answers they get. This activity is very good for reinforcing the importance of using proper SI units. It is good to let the students make this mistake. Help them recognize it and correct it.

Gravity and free fall So in reality do falling objects REALLY keep moving faster and faster? No! In real life there is air resistance. As falling objects speed up, the force of air resistance increases. When the air resistance gets as strong as the force of gravity, the falling object stops accelerating. After showing this slide, ask the students “if the acceleration becomes zero, does that mean the velocity is zero also?”

Terminal velocity Most objects reach this terminal velocity within a few seconds of being dropped. Terminal velocity is the final maximum velocity an object reaches because of air resistance. A falling human has a terminal velocity of about 140 miles per hour (or about 60 m/s).

Terminal velocity Parachutes increase air resistance. Opening a parachute changes the terminal velocity from a fast, deadly speed to a low, safe speed.

A skydiving trip When did the parachute open? When did the parachuter reach terminal velocity? Ask the students when the parachuter is at terminal velocity (at both C and E).

When can motion be treated as free fall? Free fall is NOT a good approximation for light objects, or an object with a large surface area compared to its weight (like a parachute). Free fall is a very good approximation for solid, dense objects dropped from ten meters or so. For these situations, air resistance can be ignored. 𝒂=𝒈=−𝟗.𝟖 𝒎/ 𝒔 𝟐

G U E S Solving free fall problems Be sure to GUESS Givens (what info does the problem tell you) G U E S Unknown (what are you looking for) Equation (which one do you use to find your unknown) Substitution (plug in your givens) Solution (answer with units boxed/circled)

Example 1 From what height should you drop a ball if you want it to hit the ground in exactly 1.0 second? Given: Unknown: Equation: Substitution: Solution: y = 4.9m

Example 2 Toughie! How far does an object have to fall to reach a speed of 10 m/s (neglecting friction)? Given: Unknown: Equation: Substitution: Solution: x = -5.1m

This makes sense. The ball must lose 9.8 m/s each second! An object thrown upward This ball thrown upward is in free fall as soon as the person is no longer touching it. If the ball leaves the boy’s hand with an upward velocity of 15 m/s, how fast is it moving one second later? Think: What is the sign of v0? What is the sign of a? Ask the students to make a prediction. Make sure that they recognize that the ball should slow down. This makes sense. The ball must lose 9.8 m/s each second!

An object thrown upward Here is the position-time graph for the ball thrown up at +15 m/s. What is the highest height the ball reaches? About 11.2 meters How do you know? This is the farthest point from it’s origin (0m)

Homework # 1 In each of the pictures below indicate what’s happening to the velocity of the ball along its journey & whether the acceleration is positive or negative. a. b. c.

Homework # 2 If you throw a ball straight up into the air, what is it’s Velocity at its highest point? How do you know? b. If you’re holding a marker in the air & drop it, what’s the markers initial velocity? How do you know? c. If you’re holding a ball & throw it straight up into the air, is its initial velocity 0m/s? How do you know?

Homework # 3 A pitcher on a baseball team throws a high lob across home plate. For each part of this event described below, indicate if the ball is in free fall or not (i.e. put yes or no next to each) The outfielder is winding up to throw the ball. The ball is in the air, rising to the top of its arc. The ball is in the air, descending toward the plate. The bat is connecting with the ball.

Homework # 4 A ball is thrown straight upward at 18 m/s. a.) How long does it take to reach its highest point? b.) What height does it reach, assuming it started at zero height?

Homework # 5 Say you drop two cannonballs out of a high window. The first cannonball is twice as heavy as the second. Which will hit the ground first if there is no air resistance?

Homework # 6 Two balls are thrown at the same time with the same speed. One is thrown directly downward while the other is thrown straight up. Compare their speeds when they hit the ground.