How are changes in energy and matter related
1 answer:
Answer:
According to Einstein's famous equation, matter can convert into energy (and viceversa) as follows:
where
E is the energy
m is the mass
c is the speed of light ()
Given the huge value of , we see that even a tiny amount of matter is able to release a huge amount of energy, when the whole mass is converted into energy. This is precisely what happens in nuclear reactions. For example, in the process of nuclear fusion (that occurs in the core of the stars), two light nuclei fuse together into a heavier nucleus. The mass of the final nucleus is lower than the total mass of the initial nuclei, so part of the mass has been converted into energy according to the equation above: this is why the amount of energy produced by stars is so big.
You might be interested in
The amount of heat needed to increase the temperature of a substance by 
is given by
where m is the mass of the substance, Cs is its specific heat capacity and is the increase of temperature.
If we re-arrange the formula, we get
And if we plug the data of the problem into the equation, we can find the specific heat capacity of the substance:
where m is the mass of the substance, Cs is its specific heat capacity and
If we re-arrange the formula, we get
And if we plug the data of the problem into the equation, we can find the specific heat capacity of the substance:
Answer:
Explanation:
For the simple pendulum problem we need to remember that:
,
where is the angular position, t is time, g is the gravity, and L is the length of the pendulum. We also need to remember that there is a relationship between the angular frequency and the length of the pendulum:
,
where is the angular frequency.
There is also an equation that relates the oscillation period and the angular frequeny:
,
where T is the oscillation period. Now, we can easily solve for L: