Question

How fast must an object travel for its total energy to be 1% more than its rest energy?

Answer 1

To calculate the speed at which an object must travel for its total energy to be 1% more than its rest energy, we use the equation E = mc² and set up an equation where the total energy is 1.01 times the rest energy. Solving for the speed, we find that the object must travel at approximately 0.1 times the speed of light.

Step-by-step explanation:

To calculate the speed at which an object must travel for its total energy to be 1% more than its rest energy, we need to consider the equation for the total energy of an object:

E = mc²

Where E is the total energy, m is the mass of the object, and c is the speed of light. Since we want the total energy to be 1% more than the rest energy, we can set up the following equation:

E = 1.01(mc²)

Now, we can plug in the rest energy of the object and solve for the speed:

Rest energy = mc²

0.01mc² = mc²

0.01c² = c²

0.01 = 1

c = √(0.01)

c = 0.1

Therefore, the object must travel at approximately 0.1 times the speed of light for its total energy to be 1% more than its rest energy.

Answer 2

To have a total energy 1% more than its rest energy, an object must be traveling at a relativistic speed close to the speed of light.

Step-by-step explanation:

In order for the total energy of an object to be 1% more than its rest energy, the object must be traveling at a relativistic speed. According to Einstein's theory of relativity, the total energy of an object can be calculated using the equation E = mc², where E is the total energy, m is the object's mass, and c is the speed of light. Rest energy is the energy an object possesses due to its mass at rest. To find the required speed, we can compare the kinetic energy to the rest energy.

Given that the rest mass energy of an electron is 0.511 MeV, and the kinetic energy is approximately 150% of the rest mass energy, we can set up the equation:

1.5 × (0.511 MeV) + rest energy = total energy

The object must be traveling close to the speed of light for the total energy to be 1% more than its rest energy.