Lesson 2.4 Gravitational Acceleration - AbrahamBitton - …2... · 2015-10-04 · Based on the data, what kind of motion is the bocce ball experiencing? 10. Does the data support

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Mr. Bitton Physics 1,2 Lesson 2.4 Gravitational Acceleration Student Performance Objectives Revised 7/2014 Students will recall that acceleration due to gravity near the surface of the earth is 9.8m/s2. Students will use kinematic equations to solve problems involving gravitational acceleration.

Name Date Period

Engage

A skydiver glides down to the ground. 1. What kind of motion does the skydiver experience? (stationary, uniform velocity, uniform acceleration) 2. Sketch the appearance of the following graphs for the skydiver.

A ball is dropped. 3. What kind of motion does the ball experience? (stationary, uniform velocity, uniform acceleration) 4. Sketch the appearance of the following graphs for the ball.

5. Explain why you think the motion experienced by the ball and the skydiver might be different.

Explore - Investigations In this investigation we will collect position vs. time and velocity vs. time data for a pair of stacked coffee filters and for a bocce ball dropped below a motion detector. The data collected in this experiment will provide evidence you can use to compare to your predictions in the Engage. 6. Describe the physical differences between the coffee filters and the bocce ball. 7. How might these differences affect the way the objects will fall?

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Time (sec)

Position (m)

Time (sec)

Average Velocity

(m/s)

Sketch

Sketch

Time (sec)

Position (m)

Time (sec)

Average Velocity

(m/s)

Sketch

Sketch

8. Based on the data, what kind of motion is the stack of coffee filters experiencing? 9. Based on the data, what kind of motion is the bocce ball experiencing? 10. Does the data support or reject your initial thinking about the ball and skydiver? Prepare the following set up and obtain a trace for a falling mass.

Most “plug-in” ticker tape machines make dots about once every 0.02 seconds. This is not a precise value for all machines, so our values based on these times will be approximations.

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Record the data in the table below and graph the data on the provided grid. Dot #

Approx. Time (sec)

Position (m)

5 0.1 10 0.2 15 0.3 20 0.4 25 0.5 30 0.6 35 0.7 40 0.8

11. Based on the pattern on the graph, what type of motion do you think the mass has as it falls? We’re now going to calculate and graph the average velocity of the mass as it falls. Approx.

Time (sec)

Position (from

above) (m)

Average Velocity

!

v=" in position" in time (m/s)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

12. What happens to the average velocity of the mass as it falls? 13. Does this pattern in the data support your thinking in number 10?

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The rate at which the velocity increases is defined as acceleration. In the next investigation, we will experimentally measure the value for objects falling near the surface of the earth with little air resistance.

14. Examine the image on the left, would you predict this object is moving with uniform velocity or uniform acceleration? 15. Would you predict the velocity of the ball to be increasing or remaining constant? The photo on the left is called a multiple exposure photo. A new image of the ball is recorded about every 0.045 seconds. The numbers in the image represent distances in cm. Please complete the table below using the information from this image.

16. What is the approximate value for the acceleration of the object as it falls?

In this part of the investigation, you will use a device called a picket fence dropped through a photogate sensor to get a precise measurement of the rate of acceleration experienced by an object falling near the surface of the earth.

The teacher will prepare the set up illustrated on the left. Your task will be to record displacement vs. time data from the table displayed on the projector, and graphically analyze the data.

Position (m)

Time (s)

Velocity

!

v="x"t

(m/s)

Time (s)

Final or Instantaneous

Velocity

!

vfinal=2•v (m/s2)

Time (s)

Acceleration

!

a ="v"t

(m/s2)

Time (sec)

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Sketch the following graphs for the data above.

17. Based on the patterns you see in the graphs above, what kind of motion is the falling picket fence experiencing? 18. What is the average value for the acceleration? Why is this value significant?

Explore – Notes 19. Objects with mass through the force of . 20. In the absence of , all objects near the surface of the Earth accelerate toward the center of the Earth at . 21. The mass of the object this rate. 22. This special acceleration rate is often represented with the variable “ ”. 23. Gravitational acceleration depends on the of the bodies involved and the of the objects experiencing the force.

Explain 24. In the absence of air resistance, what kind of motion do objects experience when dropped near the surface of the earth? 25. In the absence of air resistance, at what rate do objects accelerate near the surface of the earth? 26. In the absence of air resistance, does the mass of the object affect this acceleration rate near the surface of the earth? Does size matter? Galileo Galilei 1564 – 1642 was a Tuscan physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. One of the topics he explored was the rate at which objects fell near the surface of the earth. He also tested the rate at which objects of different mass fall. He conducted these famous experiments at the leaning Tower of Pisa. A version of this same experiment was conducted by Dave Scott on the surface of the moon. Watch the following video clip.

27. In the absence of air resistance, does the mass of an object affect the rate of acceleration experienced by an object? 28. A brick falls under the influence of gravitational acceleration for 3.0 sec in the absence of air resistance. Determine the displacement of the brick. a. Identify the type of motion. b. List the given terms xf = Vi = Vv = a = c. List the appropriate equation to solve for the desired term. d. Perform the necessary algebra to isolate the desired term.

e. Substitute in the given quantities and solve for the desired term and box the answer.

44.1 m 29. A ball is dropped from the roof of a building 40. meters. Determine the time of the fall. Assume no air resistance. a. Identify the type of motion. b. List the given terms xf = Vi = t = a = c. List the appropriate equation to solve for the desired term.

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d. Perform the necessary algebra to isolate the desired term. e. Substitute in the given quantities and solve for the desired term and box the answer.

2.86 s 30. A rock falls from rest off a high cliff. Determine the displacement the rock has fallen when its speed is 39.2 meters per second. [Neglect air resistance.] a. Identify the type of motion. b. List the given terms xf = vi = vf = a = c. List the appropriate equation to solve for the desired term. d. Perform the necessary algebra to isolate the desired term. e. Substitute in the given quantities and solve for the desired term and box the answer.

79.4 m 31. Determine the final speed of an object that that falls freely through a distance of 12.0 m. Neglect air resistance. a. Identify the type of motion. b. List the given terms xf = vi = vf = a = c. List the appropriate equation to solve for the desired term. d. Perform the necessary algebra to isolate the desired term. e. Substitute in the given quantities and solve for the desired term and box the answer.

15.3 m/s 32. A ball is thrown straight downward with a speed of 0.50 meter per second from a height of 4.0 meters. Determine the speed of the ball 0.70 second after it is released. [Neglect friction.] a. Identify the type of motion. b. List the given terms xf = vi = vf = a = t = c. List the appropriate equation to solve for the desired term.


8.87 m/s 33. A basketball player jumped straight up to grab a rebound. If she was in the air for 0.80 second, determine the maximum height of the jump. [Neglect air resistance.] Hint: Maximum height occurs at the halfway point in the jump and the velocity = 0 m/s at the maximum height. a. Identify the type of motion. b. List the given terms xf = vi = vf = a = t = c. List the appropriate equation to solve for the desired term. d. Perform the necessary algebra to isolate the desired term. e. Substitute in the given quantities and solve for the desired term and box the answer.

0.78 m 34. A ball thrown vertically upward reaches a maximum height of 30.0 meters above the surface of Earth. Determine the initial velocity of the ball. [Neglect air resistance.] a. Identify the type of motion. b. List the given terms xf = vi = vf = a = t = c. List the appropriate equation to solve for the desired term. d. Perform the necessary algebra to isolate the desired term. e. Substitute in the given quantities and solve for the desired term and box the answer.

24.2 m/s 35. An astronaut standing on a platform on the Moon drops a hammer. The hammer falls 6.0 meters vertically in 2.7 seconds, determine the acceleration of the hammer on the moon. [Neglect air resistance]. a. Identify the type of motion.

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b. List the given terms xf = vi = vf = a = t = c. List the appropriate equation to solve for the desired term.


1.65 m/s2

Elaborate In an experiment, a student measured the length and period of a simple pendulum. The data table lists the length (

!

l ) of the pendulum in meters and the square of the period (T2) of the pendulum in seconds2.

Directions (36–39): Using the information in the data table, construct a graph on the grid provided above, following the directions below. 36. Plot the data points for the square of period versus length. 37. Draw the best-fit straight line. 38. Using your graph, determine the time in seconds it would take this pendulum to make one complete swing if it were 0.200 meter long.

39. The period of a pendulum is related to its length by the formula: where g represents the acceleration due to gravity. Explain how the graph you have drawn could be used to calculate the value of g. [You do not need to perform any actual calculations.]

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Group Problem Solving Exoplanets are planets found around distant star systems far outside of our own solar system. There has been great excitement in the scientific community about the potential of discovering worlds that have similar properties to our own planet. If such planets exist, it may be possible for them to support life. Late last month, NASA announced the discovery of 715 more exoplanets, nearly doubling the number of planets beyond our Solar System. These newly-verified worlds orbit 305 stars, revealing multiple-planet systems outside of our own, with four of them within their stars habitable zones. It’s the single largest windfall of new confirmations at any one time, and its all thanks to a new verification technique employed by the Kepler space probe’s scientists. Nearly 95 percent of these planets are smaller than Neptune, which is almost four times the size of Earth. What’s more, this latest batch of exoplanets puts the total number of those confirmed from about 1000 to just over 1700 – and increase of 70% that occurred overnight! This discovery marks a significant increase in the number of known small-sized planets more akin to Earth than previously identified exoplanets.

These potentially habitable exoplanets would have masses similar to, but not identical to Earth. This would mean that the gravitational rate of acceleration on the surface of these planets would be different than that of Earth. Each group will be assigned an exoplanet and be asked to solve a number of problems based on an approximation of “g” on that planet (extremely rough approximations). Each group will solve the same problems using the value of “g” for earth. Each group will then present their findings to the class.

Group Planet Rough Approximation of Surface Gravity (m/s2)

1 Gliese 667C 37.2 m/s2

2 Kepler 62 e 3.78 m/s2 3 Gliese 832 C 52.9 m/s2 4 Kepler 283 C 4.92 m/s2 5 Kepler 296 f 3.06 m/s2 6 Tau Ceti e 42.0 m/s2 7 Gliese 180 C 62.7 m/s2 8 Gliese 667C f 26.5 m/s2 9 Gliese 180 b 81.3 m/s2

Surface Gravity on Earth 9.8 m/s2

!

a ="v"t

v f =vi +at

vf2 =vi

2 +2ax

xf =xi +vit +12

at 2

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Problems 1. An object is dropped from a height of 3.0 m on your planet and on earth. Determine the amount of time it would take the object to reach the surface of the planet and earth. List the given quantities for your planet. g x t

List the given quantities for earth. g x t

List the best equation to solve for the desired quantity.


Perform the necessary algebra to isolate the desired term. Perform the necessary algebra to isolate the desired term.

Substitute in the given quantities, solve the problem and box the answer.


2. An object is dropped from a height of 5.0 m on your planet and on earth. Determine the velocity of the object at the instant before it reaches the ground. List the given quantities for your planet. g vf x

List the given quantities for earth. g vf x






3. An object is thrown vertically upwards with an initial velocity of 5.0 m/s on your planet and on earth. Determine the maximum vertical height achieved by the object on your planet and on earth. Velocity final at this position = 0m/s. List the given quantities for your planet. g vi vf x

List the given quantities for earth. g vi vf x






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4. An object is thrown vertically downwards with an initial velocity of 2.5 m/s on your planet and on earth. Determine the vertical velocity of the object on your planet and on earth after 2.0 s. List the given quantities for your planet. g vi vf t

List the given quantities for earth. g vi vf t






5. You stand on a cliff on your planet and on earth. You throw an object vertically upward with a velocity of 3.0 m/s. Determine the position of the object after 4.0 s. (a negative final displacement means the object is below your position on the cliff). List the given quantities for your planet. g vi x t

List the given quantities for earth. g vi x t






6. A “friend” pulls your chair out from behind you just as you are about to sit down. You fall 0.90 m to the floor on your planet and on earth. Determine your final velocity when you reach the floor. List the given quantities for your planet. g vi vf x

List the given quantities for earth. g vi vf x






7. How would life be different on your planet? Reference your calculated values to support your answer.

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I. Gravitational Acceleration A. Objects with mass attract one another through the force of gravity. In the absence of air resistance, all objects near the surface of the Earth accelerate toward the Earth at 9.8m/s2. The mass of the object does not affect this rate. 2. This special acceleration rate is often represented with the variable “g” 3. Gravitational acceleration depends on the mass of the bodies involved and the proximity of the objects experiencing the force. a. We will study gravitational force in detail later this term.

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Lesson 2.4 Gravitational Acceleration - AbrahamBitton - …2... · 2015-10-04 · Based on the data, what kind of motion is the bocce ball experiencing? 10. Does the data support