Answer :
1. The momentum of the 1.0 gram mass moving at 0.622 kg m/s is 0.000622 kg m/s. 2. The kinetic energy of the 10 gram mass moving at 0.62c is approximately 1.555 x 10^15 J. 3. We have a contradiction, which means the initial assumption is incorrect. The total energy cannot be equal to the kinetic energy.
1: The momentum of an object can be calculated by multiplying its mass by its velocity. In this case, we have a 1.0 gram (0.001 kg) mass moving at 0.622 kg m/s. To find the momentum, we can use the formula:
Momentum = mass x velocity
Momentum = 0.001 kg x 0.622 kg m/s
Momentum = 0.000622 kg m/s
So, the momentum of the 1.0 gram mass moving at 0.622 kg m/s is 0.000622 kg m/s.
2: The kinetic energy of an object can be calculated using the formula:
Kinetic energy = 0.5 x mass x velocity^2
In this case, we have a 10 gram mass moving at 0.62c, where c is the speed of light (approximately 3 x 10^8 m/s). To find the kinetic energy, we need to convert the mass to kilograms and use the formula:
Kinetic energy = 0.5 x mass x velocity^2
Kinetic energy = 0.5 x 0.01 kg x (0.62 x 3 x 10^8 m/s)^2
Kinetic energy = 0.5 x 0.01 kg x (0.62 x 9 x 10^8 m/s)^2
Kinetic energy = 0.5 x 0.01 kg x (5.58 x 10^8 m/s)^2
Kinetic energy = 0.5 x 0.01 kg x 3.11 x 10^17 m^2/s^2
Kinetic energy = 1.555 x 10^15 J
So, the kinetic energy of the 10 gram mass moving at 0.62c is approximately 1.555 x 10^15 J.
3: The total energy of a moving neutron is five times its kinetic energy. The mass of a neutron is 1.7 x 10^-27 kg. To find the speed of the neutron, we can set up an equation:
Total energy = 5 x kinetic energy
The total energy is the sum of the kinetic energy and potential energy of the neutron. Since the potential energy is negligible in this case, we can assume the total energy is equal to the kinetic energy. Therefore:
Total energy = kinetic energy
5 x kinetic energy = kinetic energy
4 x kinetic energy = 0
We have a contradiction, which means the initial assumption is incorrect. The total energy cannot be equal to the kinetic energy.
Therefore, there is no valid solution for the given information.
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