Centripetal Force and Curving Motion - Revision history

Znjenga3: /* Summary */

2025-04-23T03:56:23Z

Summary

← Older revision		Revision as of 23:56, 22 April 2025
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	===Summary===		===Summary===

	Curved motion demands an inward net force to continuously change the direction of the object's velocity.		*Curved motion demands an inward net force to continuously change the direction of the object's velocity.

	The size of the required centripetal force depends directly on the object's speed and inversely on the radius of the curve.		*The size of the required centripetal force depends directly on the object's speed and inversely on the radius of the curve.

	Multiple physical forces (gravity, tension, friction, normal forces) can contribute to creating the necessary inward net force.		*Multiple physical forces (gravity, tension, friction, normal forces) can contribute to creating the necessary inward net force.

	~~Proper computational modeling requires keeping the force vector always directed toward the center of the circular path, accurately updating velocity and position~~.

			*Proper computational modeling requires keeping the force vector always directed toward the center of the circular path, accurately updating velocity and position.

	==Connectedness==		==Connectedness==

Znjenga3: /* Connectedness */

2025-04-23T03:55:33Z

Connectedness

← Older revision		Revision as of 23:55, 22 April 2025
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	Understanding banked curves is crucial in designing highways, racetracks, and roller coasters, ensuring safety and performance even under varying weather conditions.		Understanding banked curves is crucial in designing highways, racetracks, and roller coasters, ensuring safety and performance even under varying weather conditions.

			===Summary===

			Curved motion demands an inward net force to continuously change the direction of the object's velocity.

			The size of the required centripetal force depends directly on the object's speed and inversely on the radius of the curve.

			Multiple physical forces (gravity, tension, friction, normal forces) can contribute to creating the necessary inward net force.

			Proper computational modeling requires keeping the force vector always directed toward the center of the circular path, accurately updating velocity and position.


	==Connectedness==		==Connectedness==

Znjenga3: /* Examples */

2025-04-23T03:54:07Z

Examples

← Older revision		Revision as of 23:54, 22 April 2025
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	:::<math>F_T = 2150.7 \ \text{Newtons}</math>		:::<math>F_T = 2150.7 \ \text{Newtons}</math>

			===Extra Thought: Banked Curves===

			Sometimes, engineers tilt (bank) roads so that the normal force can help provide centripetal acceleration, reducing the reliance on friction. In a properly banked curve, even if the surface were frictionless, the horizontal component of the normal force would supply the necessary centripetal force. This allows vehicles to safely navigate curves at higher speeds without depending entirely on tire grip. Calculations involving banked curves require breaking forces into components and solving for optimal banking angles based on speed and radius.

			Understanding banked curves is crucial in designing highways, racetracks, and roller coasters, ensuring safety and performance even under varying weather conditions.

	==Connectedness==		==Connectedness==

Znjenga3: /* Main Idea */

2025-04-23T03:51:08Z

Main Idea

← Older revision		Revision as of 23:51, 22 April 2025
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	'''Real-world examples:'''		'''Real-world examples:'''

	A car turning in a circle needs static friction from the road to provide the centripetal force.		* A car turning in a circle needs static friction from the road to provide the centripetal force.

	A satellite orbiting Earth uses the force of gravity.		* A satellite orbiting Earth uses the force of gravity.

	In a spinning amusement park ride, the wall provides the inward normal force.		* In a spinning amusement park ride, the wall provides the inward normal force.

	===Mathematical Model===		===Mathematical Model===

Znjenga3 at 03:50, 23 April 2025

2025-04-23T03:50:17Z

@@ Line 1: / Line 1: @@
 [[Category:Summary]]
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 When an object is moving in vertical centripetal motion, for example when a man is swinging on a rope, the force gravity <math>mg</math> must be accounted for as well as the tension force <math> F_t</math>.
 ===Mathematical Model===
@@ Line 42: / Line 51: @@
 Normally, <math>F_{\parallel}</math> dictates the velocity of the object, while <math>F_{\perp}</math> dictates the direction of motion.
 ===Computational Model===

Ed: /* Main Idea */

2020-09-17T21:54:16Z

Main Idea

← Older revision		Revision as of 17:54, 17 September 2020
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	When an object is moving in vertical centripetal motion, for example when a man is swinging on a rope, the force gravity <math>mg</math> must be accounted for as well as the tension force <math> F_t</math>.		When an object is moving in vertical centripetal motion, for example when a man is swinging on a rope, the force gravity <math>mg</math> must be accounted for as well as the tension force <math> F_t</math>.

	~~[[File:Tarzan.jpg\|thumb\|Both the tension force as well as the gravitational force needs to be accounted.]]~~

	===Mathematical Model===		===Mathematical Model===

Laurence12799: /* Examples */

2019-07-04T01:16:52Z

Examples

← Older revision		Revision as of 21:16, 3 July 2019
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	* Problems taken from Textbook and WebAssign Resources		* Problems taken from Textbook and WebAssign Resources
	===Simple===		===Simple===
	~~'''INSERT DRAWING'''~~		[[File:CFSimpleSketch.jpeg\|200px\|right\|thumb\|A diagram of the simple example]]

	An engineer whose mass is 75 kg holds onto the outer rim of a rotating space station whose radius is 16 m and which takes 45 s to make one complete rotation.		An engineer whose mass is 75 kg holds onto the outer rim of a rotating space station whose radius is 16 m and which takes 45 s to make one complete rotation.
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	===Middling===		===Middling===
	~~'''INSERT DRAWING'''~~		[[File:CFMiddlingSketch.jpeg\|right\|200px\|thumb\|A diagram of the middling example]]

	Tarzan, whose mass is 90 kg, is swinging on a vine. At the bottom most point, the 8 m long vine breaks. At that point he is traveling at 12 m/s.		Tarzan, whose mass is 90 kg, is swinging on a vine. At the bottom most point, the 8 m long vine breaks. At that point he is traveling at 12 m/s.
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	===Difficult===		===Difficult===
	~~'''INSERT DRAWING'''~~		[[File:CFDifficultSketch.jpeg\|200px\|right\|thumb\|A diagram of the difficult example]]

	Tarzan, whose mass is 90 kg, is swinging on a vine. When the vine makes an angle of <math>\theta = 30^\text{o}</math> with the vertical, the 8 m long vine breaks. At that point he is traveling at <math>11.1 \ \frac{m}{s}</math>.		Tarzan, whose mass is 90 kg, is swinging on a vine. When the vine makes an angle of <math>\theta = 30^\text{o}</math> with the vertical, the 8 m long vine breaks. At that point he is traveling at <math>11.1 \ \frac{m}{s}</math>.

Laurence12799: /* Connectedness */

2019-07-04T00:43:05Z

Connectedness

← Older revision		Revision as of 20:43, 3 July 2019
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	==Connectedness==		==Connectedness==
	How is this topic connected to something that you are interested in?		*How is this topic connected to something that you are interested in?
	::I really enjoy sitting in rollercoasters. Every time I visit any amusement park, that is my number one object, to ride as many rollercoasters as possible. I always feel strange forces on a rollercoaster. For example, I feel a sinking feeling every time I go through a dip and feel light when the car goes over a loop. These sensations are very strange, and sometimes you can feel them in a car as well. However, now I know that these are simply forces felt when the normal force is equal to the gravitational force.		::I really enjoy sitting in rollercoasters. Every time I visit any amusement park, that is my number one object, to ride as many rollercoasters as possible. I always feel strange forces on a rollercoaster. For example, I feel a sinking feeling every time I go through a dip and feel light when the car goes over a loop. These sensations are very strange, and sometimes you can feel them in a car as well. However, now I know that these are simply forces felt when the normal force is equal to the gravitational force.

	How is it connected to your major?		*How is it connected to your major?
	::In Aerospace Engineering, centripetal force always needs to be calculated to keep a body in orbit. This can define how fast a body is to be traveling and how heavy it should be to continue in orbit. It also defines how close to the planet it is to be. The force can also be used in the calculation gravity as a propelling force, by orbiting a planet to increase velocity.		::In Aerospace Engineering, centripetal force always needs to be calculated to keep a body in orbit. This can define how fast a body is to be traveling and how heavy it should be to continue in orbit. It also defines how close to the planet it is to be. The force can also be used in the calculation gravity as a propelling force, by orbiting a planet to increase velocity.

	Is there an interesting industrial application?		*Is there an interesting industrial application?
	::Applications of centripetal forces are used mostly in mechanical systems. For example, tire manufacturers need to know the amount of centripetal force that their tires need to be made to handle. This can influence how and of what material they make their tires. A centrifuge is also a device that uses centripetal force to separate materials, and are normally used in medical and chemical applications. A centrifuge is also an amusement park ride, that lets people stick to the wall while the centrifuge spins.		::Applications of centripetal forces are used mostly in mechanical systems. For example, tire manufacturers need to know the amount of centripetal force that their tires need to be made to handle. This can influence how and of what material they make their tires. A centrifuge is also a device that uses centripetal force to separate materials, and are normally used in medical and chemical applications. A centrifuge is also an amusement park ride, that lets people stick to the wall while the centrifuge spins.

Laurence12799: /* Simple */

2019-07-03T21:38:20Z

Simple

← Older revision		Revision as of 17:38, 3 July 2019
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	::The force needed to hold on, or the centripetal force is:		::The force needed to hold on, or the centripetal force is:

	:::<math>F_c = m r \left(\frac{2\pi}{T}\right)^2 = 75* 16 \left(\frac{2\pi}{45}\right)^2 = 23.39 \ \text{Newtons}</math>		:::<math>F_c = m r \left(\frac{2\pi}{T}\right)^2 = 75 \times 16 \left(\frac{2\pi}{45}\right)^2 = 23.39 \ \text{Newtons}</math>

	===Middling===		===Middling===

Laurence12799: /* Connectedness */

2019-07-02T21:29:23Z

Connectedness

← Older revision		Revision as of 17:29, 2 July 2019
Line 155:		Line 155:
	==Connectedness==		==Connectedness==
	How is this topic connected to something that you are interested in?		How is this topic connected to something that you are interested in?
	::I really enjoy sitting in rollercoasters. Every time I visit any amusement park, that is my number one object, to ride as many rollercoasters as possible. I always feel strange forces on a rollercoaster. For example, I feel a sinking feeling ~~overtime~~ I go through a dip and feel light when the car goes over a loop. These sensations are very strange, and sometimes you can feel them in a car as well. However, now I know that these are simply forces felt when the normal force is equal to the gravitational force.		::I really enjoy sitting in rollercoasters. Every time I visit any amusement park, that is my number one object, to ride as many rollercoasters as possible. I always feel strange forces on a rollercoaster. For example, I feel a sinking feeling every time I go through a dip and feel light when the car goes over a loop. These sensations are very strange, and sometimes you can feel them in a car as well. However, now I know that these are simply forces felt when the normal force is equal to the gravitational force.

	How is it connected to your major?		How is it connected to your major?
	::In Aerospace Engineering, centripetal force always needs to be calculated to keep a body in orbit. This can define how fast a body is to be traveling and how heavy it should be to continue in orbit. It also defines how close to the planet it is to be. The force can also be used in the calculation ~~of using~~ gravity ~~was~~ a propelling force, by orbiting a planet to increase velocity.		::In Aerospace Engineering, centripetal force always needs to be calculated to keep a body in orbit. This can define how fast a body is to be traveling and how heavy it should be to continue in orbit. It also defines how close to the planet it is to be. The force can also be used in the calculation gravity as a propelling force, by orbiting a planet to increase velocity.

	Is there an interesting industrial application?		Is there an interesting industrial application?