Integrating mgR: Exploring Force and Work

In summary, the conversation discusses the concept of work in relation to external forces and the force of gravity in a problem involving a particle moving on a circle. It is clarified that work is not the same as force, and the force of gravity in this problem is mg cos(theta). The individual also asks for help understanding the integration involving the force and displacement. The conversation ends with a discussion about the range of theta and the shape of the path the particle is moving on.
  • #1
omarMihilmy
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Okay so the answer in b) is mgR how is this possible when we integrate ?

The work is the external force right?
Secondly the F inside the integral is the mg sin(theta) the force of gravity?
dr ---> pi R (semicircle)
 
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  • #2
The force, according to the problem, is [itex]mg cos(\theta)[/itex]. Are you saying you do not believe that?

I don't know what you mean by "dr--> pi R". First, in this problem you are dealing with [tex]d\vec{r}[/tex], not "dr". (Since we are moving on a circle, r is constant and dr= 0!) On a circle of radius r, [itex]x= r cos(\theta)[/itex] and [itex]y= r sin(\theta)[/itex] so that [itex]\vec{r}= r cos(\theta)\vec{i}+ r sin(\theta)\vec{j}[/itex] and [itex]d\vec{r}= -r sin(\theta)\vec{i}+ r cos(\theta)\vec{j} d\theta[/itex]

No, the "work" is NOT the "external force". Work is not force. And since there is only one force here, I don't know what you mean by "external" force.
 
  • #3
No I believe that no problem. Force done by pulling the small particle is mgcos(θ)

my problem is with the work done by that force to pull the particle is the W = ∫F.dr
This is the work done by the external force in puling the particle which should be the mgcos(θ) x the distance moved

We integrate here because the force done varies with the displacement moved due to the angle.

In the integral I will add the which force the gravitational force which is mg j
the dr⃗ =−rsin(θ)i⃗ +rcos(θ)j⃗ dθ

when we integrate this it will lead us to mgr be outside the integral and cosine(θ) which integrate to sin(θ)

Work done is mgRsin(θ) not mgR

or did he assume that the angle is 90 which is 1 ?

please help with that work part and correct me if I ma giving an faulty information
 
  • #4
omarMihilmy said:
or did he assume that the angle is 90 which is 1 ?
It says: "... from the bottom to the top", so what is the range for theta?
 
  • #5
180 sin180 is 0 so the whole thing is zero?
 
  • #6
omarMihilmy said:
180 sin180 is 0 so the whole thing is zero?
No, not 180. It's a half cylinder lying on its flat side.
 
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  • #7
Its a semi-circle with 180 degrees
A full circle is 360
Quarter is 90

Cant argue with that!
 

FAQ: Integrating mgR: Exploring Force and Work

What is the purpose of integrating mgR?

The purpose of integrating mgR is to explore the concepts of force and work in a more detailed and practical manner. Integrating mgR allows scientists to understand the relationship between the force applied to an object, its displacement, and the work done on the object.

How is mgR integrated in scientific research?

mgR is integrated in scientific research by using mathematical equations to calculate the force and work done on an object. By measuring the mass (m) of the object, the acceleration due to gravity (g), and the displacement (R), scientists can use the equation F=mgR to determine the force and work done on the object.

What are some real-world applications of integrating mgR?

Integrating mgR has various real-world applications, such as in engineering, physics, and biomechanics. For example, engineers can use this concept to design structures that can withstand certain forces and workloads, while physicists can use it to study the motion of objects in different environments. Biomechanics researchers can also use this concept to understand the forces and work involved in human movement and exercise.

How does integrating mgR contribute to our understanding of force and work?

Integrating mgR allows us to have a more quantitative understanding of force and work. It helps us to predict and analyze the behavior of objects in different situations, and to understand the relationship between force, displacement, and work. This concept also allows us to make more accurate calculations and predictions, which can be applied to various real-world scenarios.

Are there any limitations to integrating mgR?

One limitation of integrating mgR is that it assumes a constant force and a linear relationship between force and displacement. This may not always be the case in real-world situations where the force may vary or the object's motion may not be linear. Additionally, this concept does not take into account other factors such as friction, air resistance, and other external forces that may affect the motion of an object.

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