Calculating Kinetic Energy for an Object at an Angle

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Discussion Overview

The discussion revolves around calculating kinetic energy for objects projected at angles, specifically addressing how to incorporate velocity components and the relevance of angles in various physics problems. The scope includes theoretical considerations, mathematical reasoning, and conceptual clarifications related to energy conservation and projectile motion.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question whether to use the total velocity or its components when calculating kinetic energy for an object projected at an angle.
  • There is a discussion about the nature of energy as a scalar quantity, while velocity is identified as a vector, prompting questions about the relevance of angles in calculations.
  • One participant expresses confusion about the necessity of the angle in a textbook problem, suggesting that it may not be needed for calculating speed.
  • Another participant emphasizes the importance of considering both horizontal and vertical components in projectile motion and energy calculations.
  • Some participants propose that while the angle may not affect the final speed calculation, it could be significant in understanding the trajectory and energy transformations.
  • There is a suggestion that the angle is included to encourage deeper thinking about the problem rather than being strictly necessary for the solution.
  • One participant describes a method involving potential and kinetic energy to analyze the problem, while others discuss the implications of using components in different scenarios.
  • Participants explore hypothetical questions where the angle would be crucial, such as determining the angle of impact or maximum height.

Areas of Agreement / Disagreement

Participants generally agree that the angle may not be necessary for calculating final speed but express differing views on its importance in understanding the problem context and trajectory. The discussion remains unresolved regarding the necessity of using components versus total velocity in specific cases.

Contextual Notes

Some participants note that the textbook does not provide a method for the problem, only the answer, which may lead to confusion about the role of direction in the calculations. The discussion highlights the potential for different approaches depending on the specific questions posed.

Who May Find This Useful

This discussion may be useful for students and educators in physics, particularly those interested in energy conservation, projectile motion, and the application of vector components in problem-solving.

Alameen Damer
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I have a question regarding how to calculate kinetic energy. Let's say I was to find the kinetic energy of a ball shot at 180 m/s at a 45 degree angle. Do i simply sub in 180 as v (velocity) in the kinetic energy equation (1/2mv^2) or must it be split into components?
 
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Is energy a scalar or a vector quantity?
 
Scalar
 
My textbook gives me a question that reads: A baseball is thrown from a cliff of 41m at at a velocity of 22 m.s/ The ball is thrown at at 37 degree angle. What's the ball's velocity before hitting the ground?

Why do they give this angle if it has no use in this question? I know how to get the answer, but is there a time that the angle must be used?
 
Alameen Damer said:
What's the ball's velocity
Is velocity a scalar or a vector?
 
Velocity is a vector, but how does the angle play a part in it-why don't they just say it is shot at 22m/s horizontally, there is no use of the angle is there?
 
It doesn't say, "horizontally." What you've given isn't clear; the 37 degrees could be a compass heading, elevation above horizontal, declination below vertical.
 
Sorry, it is elevation above the horizontal
 
And you need to look at the horizontal and vertical components for velocities, and time of flight.
 
  • #10
Ok so i did some calculations, calculating the kinetic energy in x(22cos37) and y(22sin37) components and adding them together equals the kinetic energy when calculated from the angled velocity (22 m/s). So basically my question is, is there a reason I should calculate the kinetic energy in components as opposed to the complete vector for a problem like this?
 
  • #11
Alameen Damer said:
a reason I should calculate the kinetic energy in components
No. 222 = 484 = (1+1+1+1+1+1+1+1+1+1 + 1+1+1+1+1+1+1+1+1+1 + 1+1)2.
 
  • #12
Alameen Damer said:
Ok so i did some calculations, calculating the kinetic energy in x(22cos37) and y(22sin37) components and adding them together equals the kinetic energy
Realize that ##\sin^2\theta + \cos^2\theta = 1##.
 
  • #13
Alameen Damer said:
My textbook gives me a question that reads: A baseball is thrown from a cliff of 41m at at a velocity of 22 m.s/ The ball is thrown at at 37 degree angle. What's the ball's velocity before hitting the ground?

Why do they give this angle if it has no use in this question? I know how to get the answer, but is there a time that the angle must be used?

You have a textbook. The questions in textbooks are usually based on what the book discusses. Have you looked in the book to find out about trajectories? You could also look on this Hyperphysics Link which tells you the necessary stuff in a condensed way. If you approach this algebraically (using the formulae and symbols, instead of putting figures in, you could obtain an answer that would (or would not) contain the angle - so you could answer your own question.
 
  • #14
Alameen Damer said:
Why do they give this angle if it has no use in this question?
Note that they ask for the velocity, not simply the kinetic energy.

Of course, if all they want is the magnitude of the velocity, then perhaps you do not need the angle. That's for you to realize. There are many ways to skin a cat.
 
  • #15
Why are you using kinetic energy at all for this problem? As sophiecentaur said, you have a book: what method do they use in the sample problems?
 
  • #16
My book doesn't provide a method for a question like this, just the answer-which is given to me as 36 m/s. So I am having trouble understanding how to/if i should implement direction as they haven't given one in the answer.
 
  • #17
Alameen Damer said:
My book doesn't provide a method for a question like this, just the answer-which is given to me as 36 m/s. So I am having trouble understanding how to/if i should implement direction as they haven't given one in the answer.
What is the topic of the book chapter where this question was asked? Is it a chapter on energy conservation? Or on projectile motion?

You certainly do not need to use the angle to find the final speed. If you've covered both energy methods and projectile motion, they solve it both ways.
 
  • #18
Yes it is a unit on conservation of energy, momentum etc.
 

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  • #19
Alameen Damer said:
Yes it is a unit on conservation of energy, momentum etc.
Then why not use energy methods? (The purpose of giving the angle is to make you think! Does the answer depend on the angle?)
 
  • #20
So there is no use of the direction for the final velocity as they only ask for speed-my question still stands though, why did they give us an angle, is it ideal to be solved in terms of components?
 
  • #21
Alameen Damer said:
So there is no use of the direction for the final velocity as they only ask for speed-my question still stands though, why did they give us an angle, is it ideal to be solved in terms of components?
They gave the angle to make you think! Well then... think! :smile:

Does the angle make a difference?
 
  • #22
Yes, so the method I did was to calculate the initial potential energy, as well as the kinetic energy, add them to get the mechanical energy. Then I would sub in this value in as kinetic energy alone, as before hitting the ground it would be all converted to kinetic energy. The angle does NOT make a difference in this particular question, however is there an example of a question where it would make a difference, and thus solving in components would be ideal?
 
  • #23
I guess an energy method is implied then...

How does the speed of the object change during its flight? What makes it change? Can you think of how that relates to energy?
[Edit] looks like you got most of that.
 
  • #24
The conversion of potential energy to kinetic energy, assuming it is in a closed system with no outside forces.
 
  • #25
Alameen Damer said:
The angle does NOT make a difference in this particular question,
Good!

Alameen Damer said:
however is there an example of a question where it would make a difference, and thus solving in components would be ideal?
Sure. What if they asked: What angle does the object's velocity make when it hits the ground? Or: How high does the object rise before falling?
 
  • #26
I see, yes that would change the scenario.

In a case like that, would I need to add up the mechanical energy for the x component, and the y component, separately, then sub each into the kinetic energy equation to find the velocity in each component, then use trig to find the angle?
 
  • #27
Alameen Damer said:
In a case like that, would I need to add up the mechanical energy for the x component, and the y component, separately, then sub each into the kinetic energy equation to find the velocity in each component, then use trig to find the angle?
I would use standard projectile motion methods. Have you studied those? (Those are typically covered before getting to energy methods. They involve kinematics.)
 
  • #28
Oh okay, and yes I know them. Thank you very much for the help!
 

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