General to specific classical mechanics

In summary, the conversation discusses how to solve a problem involving a mass thrown from the origin with an initial three momentum in the y direction and subject to a constant force in the x direction. The solution involves calculating the velocity and trajectory of the mass using equations for 1D and 2D motion, as well as taking into account special relativity. The book referenced does not provide a solution, but rather guides the reader in solving the problem themselves.
  • #1
2
0
Homework Statement
Taylor Classical Mechanics 15.84
Relevant Equations
Below
Source = John R. Taylor, Classical Mechanics, page 651 + page 677

Trying to solve,

A mass [itex]m[/itex] is thrown from the origin at t=0 with initial three momentum [itex]p_0[/itex] in the y direction. If it is subject to a constant force [itex]F_0[/itex] in the x direction, find its velocity [itex]\mathbf{v}[/itex] as a function of t, and by integrating [itex]\mathbf{v}[/itex] find its trajectory.

Taylor solves this and I slowly worked this problem if mass released from rest.

$$\gamma = \sqrt{1+\bigg(\frac{Ft}{mc}\bigg)^2} $$

$$\mathbf{v}(t)=\frac{\mathbf{p}}{m\gamma}=\frac{\mathbf{F}t}{m\sqrt{1+(Ft/mc)^2}}$$

$$\mathbf{x}(t)=\frac{\mathbf{F}}{m}\left(\frac{mc}{F}\right)^2\left(\sqrt{1+\left(\frac{Ft}{mc}\right)^2}-1\right)$$

I am not sure how I could get this specific.

Thoughts=

There exists [itex] \gamma_0 [/itex] at [itex]t=0[/itex], and evolves to [itex]\gamma[/itex]. I see this [itex]\gamma_0[/itex] altering general case.
 
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  • #2
You are making it too complicated for no reason; what is speed of light doing in your attempt?
Observe vertical and horizontal motion separately and u will see what needs to be done.
#OnlyPerfectPracticeMakesItPerfect
#MathAndPhysicsHelpOnline
 
  • #3
MrsZee said:
You are making it too complicated for no reason; what is speed of light doing in your attempt?
Observe vertical and horizontal motion separately and u will see what needs to be done.
#OnlyPerfectPracticeMakesItPerfect
#MathAndPhysicsHelpOnline

I am unsure how this help.
Velocity of light is never changing.
Velocity of mass and so velocity of mass’s frame (velocity of S’ frame in special relativity language) is changing.
 
  • #4
velocity of light has nothing to do with the mass m thrown from the origin at t=0 with initial three momentum p0 in the y direction, with additional constant force in x direction.

as usual, the hardest part of the question is to understand what they are talking about.

the question is actually about projectile motion:
- x component comes from the horizontal constant force which will create displacement = Vx times the time in the air
- y component comes from p0 = m Vy, and is the subject to gravitational force; this will determine your time in the air.

hope this helps; i am not allowed here to just solve it for you.
 
  • #5
i think the OP is required to solve the problem relativistically

@yang32366
the equation you have are for 1d motion
the problem is asking you to solve 2 d version of this problem
it is like throwing a ball horizontally of a cliff. there is constant force acting on the y-axis and you give it a initial ##P_o##in the x direction except you have to do it relativistically

one tip would be to solve for ##\gamma## first
 
  • #6
when you combine two 1d analysis (x and y separately), you get 2d
 
  • #7
timetraveller123 said:
i think the OP is required to solve the problem relativistically
Yes, this is problem 15.84 in Taylor's book, which I happen to own, and appears at the end of the chapter on Special Relativity. Also, OP omitted the last sentence in the problem that reads, "Check that in the non-relativistic limit the trajectory is the expected parabola." Contrary to OP's claim, Taylor does not solve this or at least the solution does not appear in the textbook.
 

1. What is "General to specific classical mechanics"?

"General to specific classical mechanics" is a scientific approach used to describe and predict the motion of objects in the universe. It is based on the principles of Newton's laws of motion and uses mathematical equations to analyze the behavior of physical systems.

2. How does "General to specific classical mechanics" differ from other branches of mechanics?

"General to specific classical mechanics" is a broad and fundamental branch of mechanics that deals with macroscopic objects and their motion. It is different from other branches, such as quantum mechanics, which focuses on the behavior of subatomic particles, and relativistic mechanics, which studies objects moving at high speeds.

3. What are the key principles of "General to specific classical mechanics"?

The key principles of "General to specific classical mechanics" are Newton's laws of motion, which state that an object will remain at rest or continue moving in a straight line at a constant speed unless acted upon by an external force. This branch of mechanics also includes the conservation of energy, momentum, and angular momentum, as well as the principle of least action.

4. What are some real-world applications of "General to specific classical mechanics"?

"General to specific classical mechanics" has many real-world applications, including predicting the motion of planets in our solar system, designing and analyzing structures and machines, and understanding the behavior of fluids and gases. It is also used in the fields of astronomy, engineering, and physics.

5. How has "General to specific classical mechanics" evolved over time?

The principles of "General to specific classical mechanics" were first described by Sir Isaac Newton in the 17th century. Since then, it has undergone significant developments and refinements, particularly with the introduction of calculus by Gottfried Leibniz and Isaac Newton. It continues to be a foundational theory in the field of physics and has influenced other branches of mechanics and science.

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