The mechanical physics, Summaries of Physics

Download The mechanical physics and more Summaries Physics in PDF only on Docsity!

lOMoARcPSD|

J. C. Buckmaster,

The mechanical physics

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.
3. Click Play ( ) to fire the cannon. What happens? It goes over the monkey.
4. You can use the sliders to change the banana velocity ( v Initial ) 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
5. 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.

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. 2019 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 v Initial to 20.0 m/s and θ to 60.0 degrees. A. To calculate vx , multiply v Initial by the cosine of the angle: vx = v Initial • cos( θ ): 20 x cos(60) = 10.00 m/s B. To calculate vy , multiply v Initial by the sine of the angle: vy = v Initial • sin( θ ): 20 x sin(60) = 10√ = 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?)

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?
   • 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.
   • 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. 2019