North Allegheny School District / District Homepage



[pic]

Concepts of Physics

Mr. Kuffer

[pic]

A stone is thrown horizontally at a speed of +5.0 m/s from the top of a cliff 78.4 m high.

▪ How long does it take the stone to reach the bottom of the cliff?

▪ How far from the base of the cliff does the stone strike the ground?

▪ What are the horizontal and vertical components of the velocity of the stone just before it hits the ground?

Objective:

The purpose of this lab is to demonstrate an understanding of the independence of vertical and horizontal velocities of a projectile by solving a problem of a projectile launched horizontally in a lab setting.

Materials:

(Ball-bearing, race-car track, stopwatch, meter stick Styrofoam cup, lab table, calculator, class notes, text

Setup / Procedure:

To be explained in class. If absent, be prepared to gather notes from a lab partner. Remember to draw any diagram(s) when needed.

Horizontal launch (to take place in the classroom) – Using vx and dy (height) of the Ball bearing, find its dx (range), vyf, and t.

Theory:

The independence of vertical and horizontal motion and our motion equations (Use Textbook) can be used to determine the position of thrown objects. If we call the horizontal displacement dx and the initial horizontal velocity vx then, at time t, (Note: vxf = vxi)

dx = vxt

The equations for an object falling with constant acceleration, g, describe the vertical motion. If dy is the vertical displacement, the initial vertical velocity of the object is vy. At time t, the vertical displacement is

dy = vyi t + ½ gt2

Using these equations, we can analyze the motion of projectiles. (Be sure to retain the independence of the vertical and horizontal components)

[pic]

Analysis Questions:

1. The Ball bearing rolls “without friction” across the table at a CONSTANT VELOCITY. When it reaches the end of the table, it flies off and lands on the ground.

a) Draw the situation above, drawing vectors showing the Acceleration of the Ball-bearing at two positions while it is on the table and at three more when it is in the air. Draw all vectors to scale.

2. For the Ball bearing in question 1,

a) Draw vectors showing the horizontal and vertical components of the Ball bearing’s velocity at the five points.

b) Using a different color, draw the total velocity vector at the five points.

3. Determine the time the ball will be in flight.

4. Determine where the ball will land.

5. What will the final velocity be in the …

a) X direction?

b) Y direction?

6. What will the total final velocity equal?

[pic]

Name:__________ Period:_____

Projectile Motion

1. You accidentally throw your car keys horizontally at 6.0 m/s from a cliff (oops!) 64 m high. How far away from the base of the cliff should you look for your keys?

2. An airplane traveling 1001 m above the ocean at 135 km/h is to drop a box of supplies to shipwrecked victims below.

a) How many seconds before being directly overhead should the box be dropped?

b) What is the horizontal distance between the plane and the victims when the box is dropped?

3. A projectile is an object that has independent x and y components that moves through the air only under the influence of _________.

a) others b) x components

c) y components d) gravity

4. The horizontal and vertical components of a projectile are _____________.

a) the same b) dependent

c) independent d) simultaneous

6. The path of a projectile is called a ___________.

a) launch angle b) intercept

c) trajectory d) range

Study Guide:

Additional Horizontal Projectile Practice Problems

9. A stone is thrown horizontally at a speed of 5.0 m/s from the top of a cliff 78.4 m high.

a. How long does it take the stone to reach the bottom of the cliff?

b. How far from the base of the cliff does the stone hit the ground?

c. What are the horizontal and vertical components of the

stones velocity just before it hits the ground?

10. How would the three answers to problem 9 change if…

a. The stone were thrown with twice the horizontal speed?

b. The stone were thrown with the same speed, but the cliff

were twice as high?

11. A steel ball rolls with constant velocity across a tabletop

0.950 m high. It rolls off and hits the ground 0.352 m from the edge of the table. How fast was the ball rolling?

[pic]

Angular Projectile Motion

Daniel Sepulveda punts a football at 45˚ with an initial velocity of 24 m/s.

1. What is the hang time of the ball?

2. What does the punt ‘net’, assuming the return man signals for a fair catch?

3. What was the maximum height of the punt?

Name:__________ Date:_________ Period:_____

Angular Projectile Motion

5. An arrow is shot 30˚ above the horizontal. Its velocity is 49 m/s and it hits the target.

a) What is the maximum height the arrow will attain?

b) The target is at the height from which the arrow was shot. How far away is it?

6. A soccer player kicks a ball into the air at an angle of 31˚ above the horizontal and it lands at the same height from which it was kicked. The initial velocity of the ball is 35 m/s.

1. How long is the soccer ball in the air?

2. What is the maximum horizontal distance traveled by the soccer ball?

3. What I the maximum height reached by the soccer ball?

7. Romeo is chucking pebbles gently up to Juliet’s window. He is standing at the edge of a rose garden 8.0 m below her window and 9.0 m from the base of the wall. If he wants the pebbles to hit the window with only a horizontal component of velocity, how fast will the pebbles be going when they hit her window?

Extra Practice Solution

Ball Toss

When a juggler tosses a ball straight upward, the ball slows down until it reaches the top of its path. The ball then speeds up on its way back down. A graph of its velocity vs. time would show these changes. Is there a mathematical pattern to the changes in velocity? What is the accompanying pattern to the position vs. time graph? What would the acceleration vs. time graph look like?

In this experiment, you will use a Motion Detector to collect position, velocity, and acceleration data for a ball thrown straight upward. Analysis of the graphs of this motion will answer the questions asked above.

objectives

1. COLLECT POSITION, VELOCITY, AND ACCELERATION DATA AS A BALL TRAVELS STRAIGHT UP AND DOWN.

2. Analyze the position vs. time, velocity vs. time, and acceleration vs. time graphs.

3. Determine the best fit equations for the position vs. time and velocity vs. time graphs.

4. Determine the mean acceleration from the acceleration vs. time graph.

Materials

|COMPUTER |VERNIER MOTION DETECTOR |

|VERNIER COMPUTER INTERFACE |BALL |

|LOGGER PRO | |

Preliminary questions

1. THINK ABOUT THE CHANGES IN MOTION A BALL WILL UNDERGO AS IT TRAVELS STRAIGHT UP AND DOWN. MAKE A SKETCH OF YOUR PREDICTION FOR THE POSITION VS. TIME GRAPH. DESCRIBE IN WORDS WHAT THIS GRAPH MEANS.

2. Make a sketch of your prediction for the velocity vs. time graph. Describe in words what this graph means.

3. Make a sketch of your prediction for the acceleration vs. time graph. Describe in words what this graph means.

Procedure

1. CONNECT THE VERNIER MOTION DETECTOR TO THE DIG/SONIC 1 CHANNEL OF THE INTERFACE.

2. Place the Motion Detector on the table. Cover the Motion Detector with the protective cage.

3. Open the file “06 Ball Toss” from the Physics with Computers folder.

4. In this step, you will toss the ball straight upward above the Motion Detector and let it fall back toward the Motion Detector. This step may require some practice. Hold the ball directly above and about 0.5 m from the Motion Detector. Click [pic] to begin data collection. You will notice a clicking sound from the Motion Detector. Wait one second, then toss the ball straight upward. Be sure to move your hands out of the way after you release it. A toss of 0.5 above the Motion Detector works well. You will get best results if you catch and hold the ball when it is about 0.5 m above the Motion Detector.

5. Examine the position vs. time graph. Repeat Step 4 if your position vs. time graph does not show an area of smoothly changing position. Check with your teacher if you are not sure whether you need to repeat the data collection.

Analysis

1. SKETCH THE THREE MOTION GRAPHS IN YOUR LAB NOTEBOOK. THE GRAPHS YOU HAVE RECORDED ARE FAIRLY COMPLEX AND IT IS IMPORTANT TO IDENTIFY DIFFERENT REGIONS OF EACH GRAPH. CLICK THE EXAMINE BUTTON, [pic], AND MOVE THE MOUSE ACROSS ANY GRAPH TO ANSWER THE FOLLOWING QUESTIONS. RECORD YOUR ANSWERS DIRECTLY ON THE SKETCHED GRAPHS.

a) Identify the region when the ball was being tossed but still in your hands:

5. Examine the velocity vs. time graph and identify this region. Label this on the graph.

6. Examine the acceleration vs. time graph and identify the same region. Label the graph.

b) Identify the region where the ball is in free fall:

7. Label the region on each graph where the ball was in free fall and moving upward.

8. Label the region on each graph where the ball was in free fall and moving downward.

c) Determine the position, velocity, and acceleration at specific points.

9. On the velocity vs. time graph, decide where the ball had its maximum velocity, just as the ball was released. Mark the spot and record the value on the graph.

10. On the position vs. time graph, locate the maximum height of the ball during free fall. Mark the spot and record the value on the graph.

11. What was the velocity of the ball at the top of its motion?

12. What was the acceleration of the ball at the top of its motion?

2. The motion of an object in free fall is modeled by y = v0yt + ½ gt2 (equation 6), where y is the vertical position, v0y is the initial velocity in the y direction, t is time, and g is the acceleration due to gravity (9.8 m/s2). This is a quadratic equation whose graph is a parabola. Your graph of position vs. time should be parabolic. To fit a quadratic equation to your data, click and drag the mouse across the portion of the position vs. time graph that is parabolic, highlighting the free-fall portion. Click the Curve Fit button, [pic], select Quadratic fit from the list of models and click [pic]. Examine the fit of the curve to your data and click [pic] to return to the main graph. How closely does the coefficient of the t2 term in the curve fit compare to ½ g? ( 1/2 g is 4.9… what is ‘coefficient’? How well do they compare?)

3. The graph of velocity vs. time should be linear. To fit a line to this data, click and drag the mouse across the free-fall region of the motion. Click the Linear Fit button, [pic]. How closely does the coefficient of the t term in the fit compare to the accepted value for g?

4. The graph of acceleration vs. time should appear to be more or less constant. Click and drag the mouse across the free-fall section of the motion and click the Statistics button, [pic]. How closely does the mean acceleration value compare to the values of g found in Steps 2 and 3?

5. List some reasons why your values for the ball’s acceleration may be different from the accepted value for g.

[pic]

1. Label the max dy and dx.

2. Draw velocity vectors for each point of the projectile’s trajectory.

3. What is the max height of the projectile if it is launched with an initial velocity of 4.3 m/s?

4. How long is the ball in the air?

5. What is the range of the projectile if the cart is traveling at 1.2 m/s?

HINT:

“WHAT GOES UP… MUST ____________________________... BEFORE IT COMES BACK DOWN IT HAS GOT TO _____________”

Projectiles Launched at an Angle

Physics Names:

Projectile Launcher Lab

North Allegheny SH

Mr. Kuffer Period:

Determining the Range and Apex of a Projectile

Background

From class, you know that a projectile is something that is thrown or fired but not self propelled. You also know that because of gravity pulling the projectile from its straight line path, it will ideally follow a parabolic path. Also, you know that this seemingly complicated motion can be simplified by looking at the two dimensions separately. -

Purpose

The purpose of this lab is to determine the range of a projectile launcher and the height at apex. As a test, we will fire a plastic marble projectile through a hoop at the apex and into a container at the maximum range.

Procedure

Step 1-Determining the initial velocity of the launcher

Using the supplied bracket, attach a photogate to the end of the projectile launcher, as shown below.

Using gate mode, measure the time the ball will break the photogate’s beam. Prior to loading the launcher, push the ramrod into the launcher, cocking the launcher to MEDIUM RANGE. Shoot the launcher in a safe direction, and do not catch the ball. Record the broken beam time below. The diameter of the ball is exactly 1 inch or .0254 m. Determine the initial velocity of the launcher on medium range by dividing.

Step 2 - Determining range of the launcher

Clamp the launcher on the end of the table. Set the launcher’s angle so that when marble is launched on SHORT range, that it lands somewhere on the two adjacent tables.

Determine where your container should be placed to catch the marble AT THE SAME HEIGHT IT WAS LAUNCHED by resolving your initial velocity into x- and y-components, and then working out your horizontal and vertical mathematics.

(X) (Y)

Try your experiment. Did it work on the first try? What are some possible sources of error?

Continue trying and revising until you can reliably get the marble into your container.

Step 3-Determining apex of the launcher

Obtain one of the apex hoops. Place it on a ring stand as shown below.

Calculate mathematically how high the apex ring should be so that the marble can pass through the ring on route to the container. Show your work below.

Try your experiment. Did it work on the first try? What are some possible sources of error?

-----------------------

Projectile Motion

Can you get the Ball in the Cup?

Mr. Kuffer

Y

X

Y

X

13) t = 4.78 s

dx = 64.5 m

dy = 27.9 m

X

Y

[pic]

12) t = 2.76 s

dx = 64.6 m

dy = 9.27 m

X

Y

X

Y

X

Y

A) 4.0 s

B) 20 m

10 A) a) 4.0 s

b) 40 m

c) Vx = 10 m/s

Vy = 39 m/s

C) Vx = 5.0 m/s

Vy = 39 m/s

10 B) a) 5.7 s

b) 28 m

c) Vx = 5.0 m/s

Vy = 55 m/s

V = 0.8 m/s

Angular Projectile Lab

Launcher #

photogate

launcher

bracket

distance = 0.0254 m

=

velocity= m/sec

time =

Marble lands somewhere on two tables

m/sec

m/sec

m/sec

acceleration = g

acceleration = 0

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download