Acceleration and Free Fall PDF

Acceleration and Free Fall and Projectile Motion Ms. Sheila Mae Manalo Physics Teacher Review !!  Distance  Displacement  Scalar Quantity vs Vector Quantity  Speed in linear motion  Velocity in linear motion  Acceleration  Resultant Vectors Review !!  adjace...

Acceleration and Free Fall and Projectile Motion Ms. Sheila Mae Manalo Physics Teacher Review !!  Distance  Displacement  Scalar Quantity vs Vector Quantity  Speed in linear motion  Velocity in linear motion  Acceleration  Resultant Vectors Review !!  adjacent side opposite side cosine  sine  hypotenuse hypotenuse adj hyp cos  opp hyp sin  adj H.C. 63.5 cos 32 53.85 m / s, E opp V.C. 63.5 sin 32 33.64 m / s, S R  6149.12  964.2 2 6224.2 km 964.2 Tan   0.157 6149.1 1  Tan (0.157) 8.92 o Analyze !!! A ball rolling down in an incline A car moving with a constant acceleration Uniformly Accelerated An object dropped from a certain height A ball is thrown vertically straight and goes down Motion Analyze !!! A ball rolling down in an incline A car moving with a constant acceleration An object dropped from a certain height A ball is thrown vertically straight and goes down What is acceleration?  Acceleration measures the rate of change in velocity.  Average acceleration = change in velocity/ time required for change Units for acceleration v aavg  t m/s m  2 s s Sign is very important!  Acceleration has both direction and magnitude A negative value for acceleration does not always mean an object is decelerating!!  2-4 Acceleration Increasing speed and deceleration (decreasing speed) should not be confused with the directions of velocity and acceleration: Speeding up, moving to the right Slowing down, moving to the right Slowing down, moving to the left Speeding up, moving to the left Fill in the Chart Initial Velocity Acceleration Motion + + Speeding up, moving right/up - - Speeding up, moving left/down + - Slowing Down moving right/up - + Slowing Down, moving left/down - or + 0 Constant Velocity 0 - or + Speeding up from rest 0 0 Remaining at rest Motion with constant acceleration  Uniformly Accelerated Motion  Therelationships between displacement, velocity and constant acceleration are expressed by equations that apply to any object moving with constant acceleration. Different Kinemetric Equation of UAM Sample Problem 1. From rest a car accelerated at 8 m/s2 for 10 s. a. What is the position of the car at the end of 10 s? b. What is the velocity of the car at the end of 10 s? 2. With an initial velocity of 20 m/s. A car accelerated at 8 m/s^2 for 10 s. What is the position of the car after 10 s? Displacement with constant acceleration 1 xd  (vi  v f )t 2  Δd = displacement  Vi = initial velocity  Vf = final velocity  Δt = time interval Example: #1 A car accelerates uniformly from rest to a speed of 23.7 km/h in 6.5 s. Find the distance the car travels during this time. Given : Vi = initial velocity = rest = 0 km/h V = final velocity = 23.7 km/h f Δt= time interval = 6.5 s Required : Δd = displacement= distance= ? Displacement with constant acceleration  Equation 1 xd  (vi  v f )t 2  Δd = displacement  Vi = initial velocity  Vf = final velocity  Δt = time interval Problem Solving  Final velocity km 1000m 1h m conversion 23.7 x x 6.58 h 1km 3600s s  SOLUTION  (Plug in values and solve for Δd) 1 m m xd  (0  6.58 )(6.5s ) 21m 2 s s ANSWER: 21 m Velocity with constant uniform acceleration v f vi  at Vf = final velocity Vi = initial velocity a = acceleration Δt = time interval Example: #2  An automobile with an initial speed of 4.30 m/s accelerates uniformly at the rate of 3.0 m/s2. Find the final speed after 5.0 seconds. Vf = final velocity=? Vi = initial velocity = 4.3 m/s a = acceleration= 3.0 m/s^2 Δt = time interval= 5.0 s Solve  Plug in values and solve for Vf m m v f 4.3  (3.0 2 )(5.0 s ) s s Vf= 19 m/s Displacement with constant uniform acceleration 1 2 xd vi t  a (t ) 2 Δd = displacement Vi = initial velocity a = acceleration Δt = time interval Example: #2  An automobile with an initial speed of 4.30 m/s accelerates uniformly at the rate of 3.0 m/s2. Find the displacement after 5.0 seconds. Δx = displacement=?? Vi = initial velocity= 4.30 m/s a = acceleration= 3.0 m/s^2 Δt = time interval= 5.0 s Solve!  Plug in values and solve for displacement m 1 m x (4.3 )(5.0 s )  (3.0 2 )(5.0 s ) 2 59m s 2 s Final Velocity after any displacement 2 2 v v  2ax f i Vf = final velocity Vi = initial velocity a = acceleration Δx = displacement Example: A car accelerates uniformly in a straight line from rest at the rate of 2.3 m/s^2. What is the speed of the car after it has traveled 55 m?  Vf = final velocity=??  Vi = initial velocity= rest= 0 m/s  a = acceleration= 2.3 m/s^2  Δx = displacement= 55 m Solve 2 2 m 2 m m v f (0 )  2(2.3 2 )(55m) 253 2 s s s 2 2 m m v f  253 2 v f 16 s s Rearranging  Your problems won’t always be so straightforward…make sure to rearrange your equations to solve for the unknown before plugging in your numbers (with units!)  Freefall !!! Which of the two paper will fall faster ? Why? Would you agree if I say that Paper and Metal ball can fall and hit the ground at the same time? AIR RESISTANCE Air resistance is the force acting on an object that is moving through air flowing in the opposite direction. ARISTOTLE VS GALILEO Aristotle believed that an object's mass affected the rate that it would hit the ground. Galileo argued that mass did not affect the rate that an object would hit the ground. One of the first biographies of Galileo describes his famous experiment, dropping iron balls of different weights from the top of the famous leaning tower of Pisa. Galileo sought to prove that all objects fell at the same speed, regardless of their weight. Aristotle’s scientific model stated that things fell to Earth because the ‘wanted to reach their natural place’, and that the heavier an object was, the faster it would fall. Although it is simplicity itself to do the experiment that Galileo did, Aristotle apparently never did it. Aristotle’s fame was such that no one seriously challenged his assertions for over 2,000 years. Galileo’s experiment shows us the utility of gathering accurate observational data and comparing it to the predictions of scientific models. Falling Objects  FreeFall: Neglecting air resistance, all objects fall with the same constant acceleration Acceleration due to gravity m g 9.81 2 s Free Fall Acceleration However, acceleration is a vector. Gravity acts toward the earth (down) Therefore, the acceleration of objects in free fall near the surface of the earth is m a  g  9.81 2 s What we see because of air resistance… FREE FALL Example : A rock was dropped on top of the building that is 122.5 m high. How long will rock hit the ground? Learning Task 1 (UAM ) Solve for the following UMA problems. Use the GRESA format in solving the problem. 1. Bumblebee jumps straight with a velocity of 14.0 m/s. What is his displacement after 1.80 s? 2. Optimus prime coast up a hill at 11.0 m/s. After 9.3 s, he is rolling back down the slope at 7.3 m/s. What is his acceleration ? 3. Sonic ( the hedgehog) rolls up a slope of 9.4 m/s. After 3.0 s he is rolling backdown at 7.4 m/s. How far up the hill is he at this time? 4. Luigi jumps straight at 15 m/s. How high is he when he is travelling at : a.8.0 m/s upwards b.8.0 m/s downwards Performance Task 1  Title: THE EGG DROP- FREEFALL CONCEPT This experiment is designed to demonstrate the concepts of Newton’s second law, acceleration and freefall OBJECTIVES Students will apply the principles of Newton’s second law, concepts of force and acceleration due to gravity. Students will gather data and solve problems about the freefall topic Enjoy experimenting and exhibit collaboration / team efforts while doing the activity MATERIALS REQUIRED 1) Eggs (boiled ) 2) folder or cardboard 3) Filler materials like newspaper , used paper 4) Fastening materials like tape (masking tape, scotch tape), paper clips, strings, rubber bands. 5) Tools like scissors 6) timer 7) meter stick PROCEDURE 1. Using a marker make a face in your egg and name it. 😊 2. Out of your folder or cardboard , create a basket that will catch your egg for him to be safe and can be use in other distance. 3. Using a meter stick measures the height of required in the experiment (see table 1.1) and using a timer, get the time travelled by the egg. 4. Supply all the data needed in table and compute for the velocity (vf) of the egg. 5. Answer the guide questions at the end of the activity. 6. Here’s the DEAL , the freshest and uncracked egg will receive a recitation/working stub each member of the group 😊 EGG DROP - FREEFALL DISTANCE TIME Final Velocity 50 cm/ 0.5 m 80 cm/ 0.8 m 100 cm/ 1m 150 cm / 1.5 m Guide Question : 1.What is freefall in Physics? 2.What do you observe in the velocity of the egg as the distance increases? 3.If we change the boiled egg into a crumpled paper, would your data change? In what variable? 4.If air resistance is neglected ? What will happen if we simultaneously drop a paper and a boiled egg? Path of a projectile At top of path v= 0 m/s a = -9.81 m/s2 Free Fall Acceleration  At the highest point of an arc, an object has velocity = 0 m/s, acceleration is still -9.81 m/s2  An object thrown into themair is a freely falling body with vi 0 s Free Fall Problem A flowerpot falls from a windowsill 25.0 m above the sidewalk  A. How fast is the flowerpot moving when it strikes the ground?  B. How much time does a paserby on the sidewalk below have to move out of the way before the flowerpot hits the ground? Part. A.  What are we looking for: Vf  What do we know?  Displacement: -25 m  Acceleration: -9.81 m/s2  V =0 m/s i What equation should we use?? v 2f vi2  2 ax Solve the problem  2 v f  v  2ax i 2  m m v f   0   2( 9.81 2 )( 25m)  s s m v f  22.1 s Part b.  How much time before the flowerpot hits the ground?  What do we know?  Displacement= -25.0 m  Acceleration = -9.81 m/s2 v f vi  at  V initial= 0  V final = -22.1 m/s  What are we looking for: Time!  Which equation should we use?? Solve the Problem  v f vi  at v f  vi t a m  22.1  0 t  s m  9.81 2 s t 2.25s