General equation for relativistic momentum

So the correct equation is p=mv/√(1-v^2/c^2). This equation ensures that the velocity of the object will never exceed the speed of light, as the denominator will always be greater than 1, preventing the overall momentum from becoming infinite.
  • #1
bhsmith
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Homework Statement



What is the most general mathematical form for the relativistic momentum which will prevent the velocity of an object from becoming greater than c, when the object is acted on by a constant force F and the equation of motion is dp/dt=F

Homework Equations





The Attempt at a Solution



p= mv/√(1-v^2/c^2 )

I know that this equation is correct, but I'm not sure if it is the simplest form.
 
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  • #2
Hmm... well I'm not entirely sure what the question is getting at. But consider this: would p= mv/(1-v^2/c^2) satisfy the condition? (namely would it prevent the velocity of the object from exceeding c?)

Note that the question is asking for the most general form, not the simplest form.
 

What is the general equation for relativistic momentum?

The general equation for relativistic momentum is p = mv/√(1-v^2/c^2), where p is momentum, m is mass, v is velocity, and c is the speed of light.

How does the general equation for relativistic momentum differ from the classical equation?

The general equation for relativistic momentum takes into account the effects of special relativity, including the fact that mass and velocity are not independent of each other at high speeds. This differs from the classical equation, p = mv, which assumes that mass and velocity are independent.

What does the variable "c" represent in the general equation for relativistic momentum?

In the general equation for relativistic momentum, the variable "c" represents the speed of light, which is approximately 3 x 10^8 meters per second. This is a fundamental constant in physics and plays a crucial role in the theory of relativity.

What is the significance of the √(1-v^2/c^2) term in the general equation for relativistic momentum?

The term √(1-v^2/c^2) is known as the Lorentz factor, and it represents the factor by which an object's mass increases as it approaches the speed of light. This term is crucial in understanding the effects of special relativity on an object's momentum and energy.

How does the general equation for relativistic momentum impact our understanding of high-speed particles and their behavior?

The general equation for relativistic momentum has greatly impacted our understanding of high-speed particles, such as those found in particle accelerators. It has allowed us to accurately predict and measure the behavior of these particles, which has led to important discoveries in the field of particle physics.

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