Learning Goal: To apply the law of conservation of energy to an object launched upward in the gravitational Seld of the earth First, let us consider an object launched vertically upward with an initial speed v. Neglect air resistance. In the absence of nonconservative forces such as friction and air resistance, the total mechanical energy in a cosed system is conserved. This is one particular case of the law of conservation of energy Part A In this problem, you will apply the law of conservation of energy to different objects launched from the earth. The energy transformations that take place involve the objects kinetic energy K= (1/2)me and its gravitational potential energy U = mgh. The law of conservation of energy for such cases implies that the sum of the objects kinetic energy and potential energy does not change with fime. This idea can be expressed by the equation As the projectile goes upward, what energy changes take place? O Both kinetic and potential energy decrease K, + U, = Kj + U . Both kinetic and potential energy increase. where T denotes the initiar moment and T denotes the "final moment Since any two moments will work, the choice of the moments to consider is, technically, up to you. That choice, though, is usually suggested by the question posed in the problem Kinetic energy decreases: potential energy increases O Kinetic energy increases: potential energy decreases Submit Previous Answers Resuest Answer X Incorrect Try Again; 7 attempts remaining Part B Complete previous parts) Part c Complete previous partis) Part D Using conservation of energy. find the maximum height hr to which the object will rise Express your answer in terms of e and the magnitude of the acceleration of gravity g. ? Beauest Answer Submit Part E At what height h above the ground does the projectie have a speed of 0.5e? Express your answer in terms of v and the magnitude of the acceleration of gravity g. a ? Submit Reguest Answer
Learning Goal: To apply the law of conservation of energy to an object launched upward in the gravitational Seld of the earth First, let us consider an object launched vertically upward with an initial speed v. Neglect air resistance. In the absence of nonconservative forces such as friction and air resistance, the total mechanical energy in a cosed system is conserved. This is one particular case of the law of conservation of energy Part A In this problem, you will apply the law of conservation of energy to different objects launched from the earth. The energy transformations that take place involve the objects kinetic energy K= (1/2)me and its gravitational potential energy U = mgh. The law of conservation of energy for such cases implies that the sum of the objects kinetic energy and potential energy does not change with fime. This idea can be expressed by the equation As the projectile goes upward, what energy changes take place? O Both kinetic and potential energy decrease K, + U, = Kj + U . Both kinetic and potential energy increase. where T denotes the initiar moment and T denotes the "final moment Since any two moments will work, the choice of the moments to consider is, technically, up to you. That choice, though, is usually suggested by the question posed in the problem Kinetic energy decreases: potential energy increases O Kinetic energy increases: potential energy decreases Submit Previous Answers Resuest Answer X Incorrect Try Again; 7 attempts remaining Part B Complete previous parts) Part c Complete previous partis) Part D Using conservation of energy. find the maximum height hr to which the object will rise Express your answer in terms of e and the magnitude of the acceleration of gravity g. ? Beauest Answer Submit Part E At what height h above the ground does the projectie have a speed of 0.5e? Express your answer in terms of v and the magnitude of the acceleration of gravity g. a ? Submit Reguest Answer
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Educational Resource: Conservation of Energy**
**Learning Goal:**
To apply the law of conservation of energy to an object launched upward in the gravitational field of the Earth.
**Context:**
In the absence of nonconservative forces such as friction and air resistance, the total mechanical energy in a closed system is conserved. This is one particular case of the law of conservation of energy.
**Explanation:**
In this problem, you will apply the law of conservation of energy to different objects launched from the Earth. The energy transformations that take place involve the object's kinetic energy \( K = \frac{1}{2} mv^2 \) and its gravitational potential energy \( U = mgh \). The law of conservation of energy for such cases implies that the sum of the object’s kinetic energy and potential energy does not change with time. This idea can be expressed by the equation:
\[ K_i + U_i = K_f + U_f \]
where "i" denotes the "initial" moment and "f" denotes the "final" moment. Since any two moments will work, the choice of the moments to consider is, technically, up to you. That choice, though, is usually suggested by the question posed in the problem.
**Activity:**
**Part A:**
Consider an object launched vertically upward with an initial speed \( v \). Neglect air resistance.
**Question:**
As the projectile goes upward, what energy changes take place?
- Both kinetic and potential energy decrease.
- Both kinetic and potential energy increase.
- Kinetic energy decreases; potential energy increases.
- Kinetic energy increases; potential energy decreases.
*Selected answer:*
- Kinetic energy decreases; potential energy increases.
*Feedback:*
- Incorrect; Try Again. 7 attempts remaining.
**Part B & Part C:**
Complete previous part(s).
**Part D:**
Using conservation of energy, find the maximum height \( h_{\text{max}} \) to which the object will rise.
- Express your answer in terms of \( v \) and the magnitude of the acceleration of gravity \( g \).
- Input box available for submission.
**Part E:**
At what height \( h \) above the ground does the projectile have a speed of \( 0.5v \)?
- Express your answer in terms of \( v \) and the magnitude of the acceleration of gravity \( g \).
- Input box available for submission.
**Note:**
This activity offers](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e539c53-8ea0-410a-97df-bfbb76ce56a5%2F15dc50db-a9f2-465f-b7e1-78d3967a092b%2Fjvxbpu_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Resource: Conservation of Energy**
**Learning Goal:**
To apply the law of conservation of energy to an object launched upward in the gravitational field of the Earth.
**Context:**
In the absence of nonconservative forces such as friction and air resistance, the total mechanical energy in a closed system is conserved. This is one particular case of the law of conservation of energy.
**Explanation:**
In this problem, you will apply the law of conservation of energy to different objects launched from the Earth. The energy transformations that take place involve the object's kinetic energy \( K = \frac{1}{2} mv^2 \) and its gravitational potential energy \( U = mgh \). The law of conservation of energy for such cases implies that the sum of the object’s kinetic energy and potential energy does not change with time. This idea can be expressed by the equation:
\[ K_i + U_i = K_f + U_f \]
where "i" denotes the "initial" moment and "f" denotes the "final" moment. Since any two moments will work, the choice of the moments to consider is, technically, up to you. That choice, though, is usually suggested by the question posed in the problem.
**Activity:**
**Part A:**
Consider an object launched vertically upward with an initial speed \( v \). Neglect air resistance.
**Question:**
As the projectile goes upward, what energy changes take place?
- Both kinetic and potential energy decrease.
- Both kinetic and potential energy increase.
- Kinetic energy decreases; potential energy increases.
- Kinetic energy increases; potential energy decreases.
*Selected answer:*
- Kinetic energy decreases; potential energy increases.
*Feedback:*
- Incorrect; Try Again. 7 attempts remaining.
**Part B & Part C:**
Complete previous part(s).
**Part D:**
Using conservation of energy, find the maximum height \( h_{\text{max}} \) to which the object will rise.
- Express your answer in terms of \( v \) and the magnitude of the acceleration of gravity \( g \).
- Input box available for submission.
**Part E:**
At what height \( h \) above the ground does the projectile have a speed of \( 0.5v \)?
- Express your answer in terms of \( v \) and the magnitude of the acceleration of gravity \( g \).
- Input box available for submission.
**Note:**
This activity offers
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