Calculating Force in Special Relativity with Proton Velocities

• IDumb
In summary, the problem is to find the force needed to give a proton an acceleration of 4.0 x 10^19 m/s^2 for four different velocities (.09c, .4c, .7c, and .97c). The equation used is F = dp/dt = m*d/dt(yv), where B is v/c and a is acceleration. The attempt at a solution involved using the quotient rule for derivatives and simplifying the expression into an equation with γ, but there may be a better way to solve this problem.
IDumb

Homework Statement

Find the force necessary to give a proton an acceleration of 4.0 1019 m/s2 when the proton has the following velocities (along the same direction as the force).

We're covering special relativity and due to my lack of a brain I can't figure this simple problem out.

Velocities are .09c and .4c (I have answers the homework website likes for these ones because the v/c isn't doing much to y?)

and .7c and .97c, which I can't get right.

F = dp/dt
P = ymv
(y is gamma)

The Attempt at a Solution

I tried using the quotient rule for derivatives, and got an eqn that, when plugging in the given velocities, came up with answers that it marked as correct for the first 2, but not for the 2nd 2.

F = dp/dt = m*d/dt(yv)
(B is v/c) (a is acceleration)
F = m[(a*sqrt(1-B^2) + ((1-B^2)^-.5)(B^2)(A)]/(1-B^2)

There must be a better way to do this problem... if anyone can help I would appreciate it, very angry with this problem. Thanks.

IDumb said:
F = dp/dt = m*d/dt(yv)
(B is v/c) (a is acceleration)
OK.
F = m[(a*sqrt(1-B^2) + ((1-B^2)^-.5)(B^2)(A)]/(1-B^2)
Not quite sure I understand that last step. Try to simplify this expression into some final form. (Express everything in terms of γ.)

What is special relativity force?

Special relativity force is a concept in physics that explains how objects move and interact with each other in relation to their relative velocities. It is based on Albert Einstein's theory of special relativity, which states that the laws of physics are the same for all observers in uniform motion.

How does special relativity force differ from classical mechanics?

Special relativity force differs from classical mechanics in that it takes into account the effects of an object's velocity on its mass, length, and time. In classical mechanics, these properties are considered constant, but in special relativity, they are relative to the observer's frame of reference.

What is the role of the speed of light in special relativity force?

The speed of light, denoted as c, is a fundamental constant in special relativity force. It is the maximum speed at which an object can travel in the universe and serves as a crucial component in equations that describe the relationship between an object's mass, velocity, and energy.

Can special relativity force be observed in everyday life?

Yes, special relativity force can be observed in everyday life, particularly at high speeds or in extreme conditions. For example, GPS satellites must take into account the effects of special relativity on time dilation in order to accurately determine location on Earth. Additionally, particle accelerators and nuclear reactors rely on special relativity principles to function.

What are some practical applications of special relativity force?

Special relativity force has several practical applications, including in the fields of nuclear energy, particle physics, and space travel. It also helps us understand the behavior of objects at high speeds and in extreme conditions, which is essential for advancements in technology and scientific research.

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