Feed The Monkey Gizmo For Student\'s Understanding PDF

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Vocabulary: acceleration, force, friction, mass, newton, Newton’s first law, Newton’s second law, Newton’s third law, velocity...

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Student Exploration: Feed the Monkey (Projectile Motion) Vocabulary: acceleration, free fall, trajectory, vector, velocity Prior Knowledge Questions (Do these BEFORE using the Gizmo.) Eccentric billionaire Veda Hussert has invented a “banana cannon” to help feed the monkeys on her personal wildlife preserve. To feed a monkey high in the trees, simply aim the cannon at the monkey and fire a banana! Unfortunately, the noise of the cannon frightens the monkeys, and they drop out of the tree when they hear the sound. 1. To hit a falling monkey with a banana, where should Veda aim? (Circle your choice.) A. Above the monkey B. Below the monkey C. Directly at the monkey

2. Explain your choice: The banana and the monkey fall at the same speed.

Gizmo Warm-up The Feed the Monkey Gizmo shows a banana cannon and a monkey. When the cannon fires, the startled monkey drops from the branch. 1. Click Play (

) to fire the cannon.

What happens? It goes over the monkey. 2. You can use the sliders to change the banana velocity (vInitial) and cannon angle (θ). (You can also drag the cannon barrel.) Make adjustments until the monkey catches the banana. What was the velocity and angle that you used? 17 m/s and 32 degrees 3. Now try increasing and decreasing the velocity. Assuming the banana is moving fast enough to reach the tree, does the monkey still catch the banana? Describe your findings. Sustaining the cannon angle at 32 degrees, a change in the banana’s velocity did still reach the monkey. However, the lowest velocity that allowed the banana to reach the monkey was 17 m/s and the highest velocity that allowed the banana to reach the monkey was 29 m/s.

Activity A: Banana catchers

Get the Gizmo ready: ∙ Click Reset ( ). ∙ Set the initial velocity (vInitial) to 26.0 m/s.

Question: Where should you aim to hit the monkey with a banana? 1. Experiment: Turn on Show target line. Experiment with the Gizmo, trying several different cannon locations and launch angles. Try aiming above, below, and directly at the monkey. A. What always happens when you aim above the monkey’s head? At 37 degrees (aimed above the head), the banana goes over the monkey. B. What always happens when you aim below the monkey’s feet? At 27 degrees (aimed below the feet), the banana goes under the monkey. C. What always happens when you aim at the monkey’s body? At 32 degrees (aimed at the body), the monkey catches the banana.

2. Predict: How do you think changing the banana velocity will affect your results?

I predict that changing the banana’s velocity will not affect the results.

3. Test: Click Reset. Turn on Show grid, and drag the cannon to the point (25, 0.0) on the grid. Aim the cannon at the monkey, and try vInitial values of 15.0, 20.0, 25.0, and 30.0 m/s. How did the banana velocity affect the results of the experiment? With the canon aimed at the body of the monkey, the changes in banana velocity did not affect the results. The monkey caught the banana each time.

4. Observe: Click Reset, and turn on Show path. Drag the cannon to (0.0, 16.0) so that it is at the same level as the monkey. Set vInitial to 25.0 m/s, and θ to 0.0 degrees. Click Play. The lines represent the trajectories, or paths, of the banana and monkey. The dots on the

lines show positions every 0.15 seconds. Compare the dots for the banana and monkey. A. What do you notice about the height of the dots on each trajectory? The height of the dots on each trajectory was the same. B. At any given time, what can you say about the heights of the banana and monkey? They are identical.

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Activity B: Velocity vectors

Get the Gizmo ready: ∙ Click Reset, and drag the cannon to the ground. ∙ Turn off Show grid and Show path. ∙ You will need a scientific calculator for this activity.

Introduction: Velocity is an example of a vector quantity because it describes the speed and direction of an object. The velocity of an object through space can be shown by two components: a horizontal component (vx) and a vertical component (vy). Question: How does the velocity of an object change as it flies through space? 1. Observe: Turn on Show velocity components, and set θ to 45.0 degrees. Click Play, and focus on the blue and red arrows that represent the vertical and horizontal components of the banana’s velocity. A. As the banana flies through space, what do you notice about the blue (vertical) arrow? With the banana velocity set to 15 m/s, the blue arrow first points upwards, then shortens and points downwards. The velocity component of the vertical component starts at 10.61 m/s and ends at -9.88 m/s. It decreases over time. B. As the banana flies through space, what do you notice about the red (horizontal) arrow? With the banana velocity set to 15 m/s, the red arrow stays the same throughout. The velocity component of the horizontal component stays at 10.61 m/s for the whole duration. C. Try other velocities and launch angles. Do these results hold up?

With the banana velocity set at 20 m/s and the launch angle at 58.0 degrees (aiming directly at the monkey's body), the banana is caught. When the banana is caught, all the velocity components finish at 0.00 m/s. 2. Calculate: You can use trigonometry to find the initial horizontal and vertical components of the banana’s velocity. Take out your calculator now. Click Reset, and turn off Show velocity components. Set vInitial to 20.0 m/s and θ to 60.0 degrees. A. To calculate vx, multiply vInitial by the cosine of the angle: vx = vInitial • cos(θ): 20 x cos(60) = 10.00 m/s B. To calculate vy, multiply vInitial by the sine of the angle: vy = vInitial • sin(θ): 20 x sin(60) = 10√3 = 17.32 m/s C. Turn on Show velocity vectors. Were you correct? Yes I was correct. 3. Analyze: An object flying through the air is said to be in free fall. As you observed, the horizontal component of velocity (vx) does not change as the object moves, but the vertical component (vy) decreases over time. (Note: Air resistance is not included in this model.) A. What force causes vy to change as the banana travels? Gravity causes vy to change as the banana travels. B. Why doesn’t vx change as the object travels? (Hint: Are there any horizontal forces on the banana after it leaves the cannon?)

No, there are no horizontal forces on the banana after it leaves the cannon- there is no air resistance. Activity B (continued from previous page) 4. Set up Gizmo: Acceleration is a change in velocity. Both the banana and monkey undergo a downward acceleration due to the force of gravity. To calculate the acceleration of a falling object, divide the velocity change by the time interval. a = (vCurrent - vInitial) / t Check that vInitial is set to 20.0 m/s and θ to 60.0 degrees. Record the initial vertical velocity of the banana and monkey in the first row of the table below. Time

vy (banana)

vy (monkey)

0.00 s

17.32 m/s

0.00 m/s

0.79 s

9.58 m/s

-7.74 m/s

5. Gather data: Click Play, and then click Pause ( ) before the monkey and banana hit the ground (or each other). Record the time, vy (banana), and vy (monkey) in the second row of the table above.

6. Calculate: For each object, calculate the velocity difference by subtracting the initial velocity from the final velocity (your answer should be a negative number). Then divide these numbers by the time to find the acceleration of each object. (Units of acceleration are m/s2.) Banana velocity change: 9.58 m/s - 17.32 m/s Monkey velocity change: = -7.74 m/s -7.74 m/s - 0.00 m/s Banana acceleration:

= -7.74 m/s Monkey acceleration:

-7.74 m/s / 0.79 s = -9.8 m/s2

= -7.74 m/s / 0.79 s = -9.8 m/s2

7. Analyze: What do you notice about the banana and monkey’s acceleration?

The banana and the monkey’s acceleration are equal.

8. Think and discuss: Based on what you have learned about velocity and acceleration in this lesson, why should you aim directly at the monkey if you want it to catch the banana?

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The constant acceleration due to gravity affects both the monkey and the banana in the same way. Gravity is the only force that will affect when the banana reaches the monkey. Since there is no air resistance (or other force) that affects the horizontal velocity and path, aiming directly at the monkey will always result in it catching the banana.

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The speed of the banana does not matter when the canon is initially aimed at the monkey. An increase in banana velocity will result in the monkey catching the banana at a higher point, while a decrease in banana velocity will result in the monkey catching the banana closer to the ground. As gravity sets forth the same acceleration on both the banana and the monkey, their vertical positions will always be linked if aimed directly at the monkey.

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