2) Let s denote the mass of a stationary object as m0 and the mass of the same object but moving at a velocity

Мурчик

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v as m1. According to the theory of relativity, the mass of the moving object will be greater than the mass of the stationary object. This phenomenon is known as relativistic mass. Let"s explore the concept of relativistic mass and how it is related to the velocity of an object.

According to Einstein"s theory of relativity, the mass of an object increases as its velocity approaches the speed of light, which is denoted as c. This means that the mass of an object is not constant but depends on its velocity.

The equation that relates relativistic mass (m1) and rest mass (m0) is given by:

\[m1 = \frac{{m0}}{{\sqrt{{1 - \frac{{v^2}}{{c^2}}}}}}\]

Where:
- m1 is the relativistic mass of the object
- m0 is the rest mass (or mass at rest) of the object
- v is the velocity of the object
- c is the speed of light in a vacuum (\(c ≈ 3 × 10^8\) m/s)

Let"s consider an example to better understand this concept. Suppose we have a stationary object with a rest mass of 1000 kg (m0 = 1000 kg). If this object starts moving with a velocity of 0.9c or 90% of the speed of light, we can calculate its relativistic mass using the formula:

\[m1 = \frac{{m0}}{{\sqrt{{1 - \frac{{v^2}}{{c^2}}}}}}\]

Substituting the values:
m0 = 1000 kg
v = 0.9c
c ≈ 3 × 10^8 m/s

\[m1 = \frac{{1000}}{{\sqrt{{1 - \frac{{(0.9c)^2}}{{c^2}}}}}}\]

Now, let"s simplify the equation and calculate m1:

\[m1 = \frac{{1000}}{{\sqrt{{1 - 0.9^2}}}}\]

\[m1 = \frac{{1000}}{{\sqrt{{1 - 0.81}}}}\]

\[m1 = \frac{{1000}}{{\sqrt{{0.19}}}}\]

\[m1 ≈ 1061.29\]

So, the relativistic mass of the object moving at a velocity of 0.9c is approximately 1061.29 kg.

From this example, we can observe that as the velocity of an object approaches the speed of light, its relativistic mass becomes significantly greater than its rest mass. This relativistic mass increase is a result of the energy associated with the object"s motion.

It is important to note that the concept of relativistic mass is not commonly used in modern physics. Instead, physicists prefer to use the concept of relativistic momentum and energy, which are more fundamental quantities. However, the concept of relativistic mass can still be useful in certain contexts and understanding the relationship between mass and velocity in relativistic scenarios.