The mass of an object is a measure of what?
the choices are..
acceleration
force
inertia
velocity.
Inertia is the resistance of any physical object to a change in its state of motion.
In Newton’s equation, Force = mass * acceleration, acceleration is a change in the state of motion. Force is the cause of the change in the state of motion.
MASS IS A MEASURE OF AN OBJECT’S RESISTANCE TO ACCELERATION!!
Objects with greater mass require more force to accelerate than objects with less mass, because objects with more mass have more inertia.
The equation below is very helpful
Mass = rest mass ÷ [1 – (v^2 / c^2)]^ 0.5
Assume v is always less than c.
Then v^2 / c^2 is always a fraction that is less than 1. (the numerator is less than the denominator)
This is Einstein’s equation for the mass of an object versus the velocity of the object. As the velocity increases, the mass of the object increases. The number of atoms does not increase. The number of protons, neutrons, and electrons does not increase.
The object is not any bigger. The number of atoms in the object is the same as when the object was sitting on my desk. What matters, is not that the amount of matter really has not changed, what really matters, is that the matter is becoming more difficult to accelerate.
The object’s resistance to change of motion is increasing, so the inertia of the object is increasing. As the velocity of an object approaches the speed of light; the answer to the equation below approaches infinity.
Mass = rest mass ÷ [1 – (v^2 / c^2)]^ 0.5
The state of rest or uniform motion is the MOST STABLE state of an object. This is a low energy state. As a force is exerted to accelerate the object the velocity of the object increases, so the kinetic energy increases. This is a high energy state. We know that objects with extra energy are less stable. Objects moving at higher velocity have more energy, so they are less stable, so the mass is greater because the inertia is greater.
Another example is nuclear decay!
The reaction equation is shown below:
Am-241 → Np-237 + α + 5.49 * 10^11 Joules of energy
Mass of 1 mole of Am-241 nuclei = 241.0567 grams
Mass of 1 mole of Np-237 nuclei = 237.0480 grams
Mass of 1 mole of alpha particles = 4.0026 grams
Total mass of products = 237.0480 + 4.0026 = 241.0506 grams
Mass of reactant – total mass of products = 241.0567 – 241.0506 = 0.0061 grams
As this reaction occurred, 0.0061grams seems to have disappeared.
Yet, no particles have disappeared!
The nucleus of an Americium-241 atom contains 95 protons and 146 neutrons.
The nucleus of a Neptunium-237 atom contains 93 protons and 144 neutrons.
The alpha particle contains 2 protons and 2 neutrons.
Nuclear particles before the reaction = 95 protons and 146 neutrons.
Nuclear particles after the reaction = (93 + 2) protons and (144 + 2) neutrons = 95 protons and 146 neutrons
All the protons and neutrons are accounted for, NO PARTICLES HAVE DISAPPEARED!! No protons or neutrons are lost!!!
Where did this energy come from!!!
According to Einstein’s equation:
Energy = mass * c^2
Mass = 0.0061 grams = 6.1 * 10-6 kg
c = speed of light = 3 * 10^8 m/s
Energy = 6.1 * 10-6 * (3 * 10^8)^2 = 5.49 * 10^11 Joules
As the nucleus of an Americium-241 atom under goes radioactive decay, it becomes more stable. The release of 5.49 * 10^11 Joules of energy is how the nucleus becomes more stable!
The energy of the nucleus of Neptunium-237 is 5.49 * 10^11 Joules less than the energy of the nucleus of Americium-241; so, the nucleus of Neptunium-237 is more stable than the nucleus of Americium-241.
So, the nucleus of Neptunium-237 has less than the inertia of the nucleus of Americium-241.
Since mass measures inertia, the mass of the nucleus of Neptunium-237 is less than the mass of the nucleus of Americium-241.
The relationship between mass and inertia helps us understand how nuclear energy is produced without destroying any elementary particles.
And
The relationship between mass and inertia helps us understand how Einstein’s equation is used to determine the amount of energy which is produced when the “MASS” of the elementary particles actually decreases.
I hope this helps!