Application of Mathematics on physics:

Mechanics

Waves

Heat

Energy

We will show some of the example of the use of mathematics in physics.

The application on physics:

Example one:(例句一 )

A student throws a phone upward at an initial

velocity from his compartment. The phone returns

to his hand after 3s. Neglect air resistance.

Determine the initial velocity:

Take upward direction as positive.

Because the phone return to his hand in same velocity therefore v=-u.

By v=u+at,

-u=u+(-10)x3

u=15m/s

In the above example, mathematics can enable us to find result without experiment.

Example two :(例句二 ) A dog have a mass 20 kg, running at 5m/s,crush with a cat of mass 15kg which was running at 3m/s.Find the common velocity of them just after the collision if they locked together after the collision . The total momentum before the collision (initial momentum) =(20)(5)+(15)(-3) =55 kg m/s The total momentum before the collision (final momentum) =(20+15)(v) by the law of conservation of momentum, initial momentum =final momentum: 55 = (20+15)(v) v=1.57m/s Therefore,they move at original direction at a common velocity of 1.57m/s.

From the above ,mathematics can solve the momentum problem..

Example three:

There is a wave has wave length of 3m and frequency of 50Hz

What is the wave speed?

Apply v= fλ

v = (50) (3)

v= 150m/s

So the wave speed is 150m/s.

From above experiment, we can know mathematics can enable us to get experiment result which is hard to record.

Example four:

2-kg of water need to heat from 25oc to 78oc, how many energy is need?(assume no heat lost) The heat capacity of water 4200Jkg-1 oc-1

apply E= mc

J

So mathematics can enable us to get heating experiment’s result, since it is impossible to measure energy correctly by meter!!!!!!

Sometimes physics involve geography issue, for example the scale of the strength of earthquake is called Richter Scale, the Richter Scale is calculate in common logarithm(log10), for example level 5 earthquake is ten times to level 4 earthquake, in the same way of calculation, level 5 of earthquake is 100 times of level 3 earthquake.