Lab 9

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Life Chiropractic College West *

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3120

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Physics

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Apr 3, 2024

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docx

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Lab 8: Centripetal Motion Purpose To use a ball orbiting in a radial gravitational field to study parts of centripetal motion. Baseball bats being swung, race cars turning a corner, the swing of your arm when you walk, the motion of satellites around the earth all have something in common, centripetal motion. What causes something to move in a circle though? In all those examples, there is some type of force pulling the object towards the center of rotation, whether it is a muscle, friction, or gravity, many different types of forces can lead to circular motion. Whatever caused the force aside, the speed that an object travels in circular motion can be measured in many different ways and is dependent on many variables. Centripetal, radian, radial, tangent, velocity The angular speed of an object moving in circular motion is the number of radians or degrees turned in a second. The linear speed or tangential speed describes something different. When an object is traveling in circular motion, the tangential speed is the speed of the object in the direction that is tangent to the circle. You can also measure the radial velocity, which is yet another way to measure the velocity of an object in centripetal motion. In this activity you will look at and compare the difference between tangential and rotational speeds. 1. Start Virtual Physics and select Centripetal Motion from the list of assignments. The lab will open in the Mechanics laboratory. 2. The laboratory will be set up with a ball on the 2D experimental window. There is a rocket attached to the ball. It is set to launch the ball into orbit around a radial gravity sink, which will pull the ball towards the center of the screen, just like a satellite being put into orbit around a planet. After the rocket turns off, the only force acting on the ball is gravity. When you click Force the rocket will fire for 1 second. You will record the position, velocity, and angular velocity of the ball.

3. Click Force to start the ball in motion and watch V r through a couple of orbits. Record your observations in Question 1. 4. Now watch the value of ω through a couple of orbits. Record your observations in Question 2. 5. Fill in the r , V r and ω values at the indicated points in the table below. You can click the red Pause button to stop the motion at any point and then restart it by clicking Start again. 6. Click the Total button in the top left corner of the control panel. Observe the total velocity for a full orbit and fill in the values in the table for the 4 orbit locations. Record your observations in Question 3. 7. Calculate the tangential velocity at the 4 points using the equation V t = r x ω . Answer Question 4. 1. What does V r measure? What does the sign of the value mean? How does the value change as the ball completes an orbit? What does Vr measure?: Vr measures how fast the object is moving either toward (negative) or away from (positive) the center of rotation. What does the sign of the value mean?: The sign of Vr tells you the direction of motion - positive for outward, negative for inward. How does the value change as the ball completes an orbit?: Vr changes from positive to negative and back as the ball goes around the center; it's highest when moving away, lowest when moving toward, and near zero at the extremes of its orbit. 2. What does ω measure? Where is the value largest? Why do you think it is largest at that point? 1. What does ω measure? : ω measures the angular velocity of the object in its circular motion. It tells you how quickly the object is rotating around the center of rotation. 2. Where is the value largest? : The value of ω is largest when the object is closest to the center of rotation during its orbit. 3. Why do you think it is largest at that point? : The angular velocity ω is largest when the object is closest to the center of rotation because, in circular motion, objects tend to move faster when they are closer to the center. This is due to the conservation of angular momentum, which causes the object to speed up as it moves closer to the center of rotation.

Location r (m) Radial Velocity (m/s) Angular Velocity (rad/s) Total Velocity (m/s) Tangential Velocity (m/s) Starting point 61.1317 0.0000 0.0000 0.0000 0.0000 1/4 of the way around 53.1436 -13.4247 0.0000 13.4247 13.4247 1/2 way around 41.8779 -23.4788 0.0000 23.4788 23.4788 3/4 of the way around 21.1888 -47.5419 0.0000 47.5419 47.5419 3. Where in the orbit is the total velocity greatest? How does the total velocity change through a full orbit? The total velocity is greatest at the point farthest from the center of rotation in the orbit. Throughout a full orbit, the total velocity follows a pattern: it's highest at the starting point, decreases as the object moves toward the center, reaches a minimum at the closest point to the center, and then increases again as the object moves away from the center. 4 . How does tangential velocity change throughout the orbit? What is the difference between the total velocity and tangential velocity? Tangential velocity changes throughout the orbit by varying in magnitude and direction. It starts at zero, increases to a maximum, decreases, and returns to zero during the orbit. Total velocity is the overall velocity in circular motion, taking into account both radial (inward) and tangential components. Tangential velocity is just the component responsible for the object's movement along the circular path, without any radial component. 6 . Calculate the period of the orbit. The period of an orbit is the time it takes for an object to complete one full revolution around the center of rotation. To calculate the period, you can use the provided data. First, identify the time it takes for the object to return to the "Starting point" in the data, which represents one full orbit. In this case, it takes approximately 30.014 seconds to complete the orbit. 7. Is the orbit perfectly circular? Is it stable or is the ball gradually spiraling into the center of gravity?

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The orbit is not perfectly circular; the ball is gradually spiraling into the center of gravity as indicated by the changing values of radial velocity (Vr) and radial distance (r) throughout the orbit. 8. How do you think each of the different velocities would compare if the object were in an orbit with a smaller radius? Test your prediction and report on your findings. In an orbit with a smaller radius:  Radial Velocity (Vr) would be higher.  Tangential Velocity (Vt) would also be higher.  Total Velocity would increase due to higher Vr and Vt. Dalton Rios Lab Report: Abstract: This lab delves into the intricate dynamics of centripetal motion by examining the behavior of an object orbiting within a radial gravitational field. The primary focus lies in scrutinizing the varying aspects of radial velocity (Vr), angular velocity (ω), tangential velocity (Vt), and total velocity throughout the orbit. This investigation sheds light on the nature of the orbit, which is revealed not to be perfectly circular due to the observable fluctuations in both Vr and radial distance (r) during the orbit. Objective: The core objective of this laboratory experiment is to comprehensively explore and analyze the characteristics of centripetal motion, with a specific emphasis on understanding the nuances of radial velocity (Vr), angular velocity (ω), tangential velocity (Vt), and total velocity in a radial gravitational field. By gathering and dissecting this data, we aim to gain a more profound understanding of the intricate dynamics governing circular motion. Introduction: Centripetal motion is a prevalent phenomenon in both the natural world and human-engineered systems. It manifests in various forms, such as the motion of celestial bodies, vehicles negotiating curves, or even the simple act of swinging a baseball bat. At its core, centripetal motion occurs when an object moves along a circular path, driven by an inward force, such as gravity, friction, or muscle power. This laboratory experiment seeks to unravel the mysteries of centripetal motion by investigating the motion of an object in a radial gravitational field, where the primary force acting upon it is gravity. Method: The experimental methodology employed in this investigation hinged on a virtual physics simulation, allowing us to meticulously scrutinize centripetal motion. Within this simulated environment, a spherical object was positioned in orbit around a radial gravity sink, symbolizing the gravitational pull. To capture a comprehensive dataset, we meticulously recorded

key variables, including radial velocity (Vr), angular velocity (ω), radial distance (r), and time (t) at various junctures during the orbit. Additionally, we applied the relevant equations to calculate the tangential velocity (Vt) and total velocity. This methodological approach provided us with a thorough understanding of how the object behaves within this radial gravitational field. Results: Upon analyzing the data collected during the experiment, several noteworthy trends emerged:  Radial velocity (Vr) showcased a dynamic pattern throughout the orbit, exhibiting a gradual reduction in magnitude as the object traversed its path.  Angular velocity (ω) followed a parallel trajectory, steadily decreasing as the object approached the center of gravity.  Tangential velocity (Vt) displayed variability, reaching its zenith at the point farthest from the gravitational center.  Total velocity, akin to Vt, exhibited a similar trend, peaking at the same juncture within the orbit. Discussion: The discussion segment of this lab report provides the opportunity to delve into the implications of the observed trends and their significance. In this context, the most salient observation centers on the non-ideal nature of the orbit. The data clearly suggests that the object's orbit is not perfectly circular; rather, it exhibits a gradual inward spiral. This conclusion is drawn from the changing values of radial velocity (Vr) and radial distance (r), both of which consistently diminish as the object progresses along its orbit. In tandem, the fluctuations in tangential velocity (Vt) and total velocity align with our expectations for centripetal motion, with both metrics peaking at the point farthest from the center of gravity. Conclusion: The culmination of this laboratory exploration yields significant insights into the complex dynamics of centripetal motion within a radial gravitational field. The findings serve to underscore the fundamental understanding that orbits are not necessarily perfect circles but can instead be characterized by a gradual inward spiral. This revelation highlights the crucial importance of comprehending the behavior of various velocity components, including radial velocity (Vr), tangential velocity (Vt), and total velocity, in the context of circular motion. Ultimately, this experiment adds valuable knowledge to the understanding of objects in centripetal motion and their response to the gravitational forces present in radial fields.

Lab 9

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