“A 2 kg ball is dropped from 25 m up. How fast is it going 5 meter above the ground, no air friction?”

One way to approach the problem is to use conservation of energy. Part of the gravitational potential energy is converted to kinetic energy. Given the directions, we can assume conversation of energy.

The energy converted is the change in height multiplied by gravity multiplied by the mass. That same amount of energy will become kinetic energy.

So you can set that amount of energy equal to the equation for kinetic energy and solve for the velocity.

ball dropping energy conversion

You could also use the kinematic equations. The initial velocity would be zero.

two linear motion equations

“How many US gallons of water are in one metric ton?”

You can input this question directly in Google verbatim and it will output your answer.

Google has not always been able to do this, but it has been able to do this for at least a few years. I could use this functionality as an undergrad and as a graduate student.

Google is aware of many physical quantities.

gallons in a ton

“How do you calculate the volume of a liquid? What’s the unit of measurement?”

Volume is basically the three dimensional space that something fills. So you can place the liquid in a container with standardized markings.

Volume can change based on temperature and pressure though.

The SI unit of volume is the cubic meter. Other units used can be cubic centimeters, liters, etc. Often we choose the units based on the situation. To use units in an equation though, it’s often better to start with SI units.

You can convert between units of volume using ratios. Another simple way to convert units is just to use Google,

You can input something like this:

“Two liters is how many gallons”

And Google will tell you.

Example:

volume liters gallons

You can also calculate the volume if you know the density and mass. (Again, temperature and pressure are also factors).

Density = mass/volume

Volume = mass/density

How are Decibels Measured?

You would need a device to measure the intensity of the sound.

Intensity is the power divided by area, it’s similar conceptually to pressure.

Once you have the intensity, you would use an equation to get decibels, which are often a convenient unit for measuring sound.

decibels sound intensity

I0 is the reference intensity, which is often 10^-12 W/m^2. That is the threshold for human hearing.

You can imagine the intensity as being the power of the sound propagating outward from a point like a sphere if the sound spreads equally in all directions. Speakers can also be more directional. The logarithm is base 10 and you multiply by ten in front because of the prefix deci.

A Song of Ice and Steam

0.6 kg of ice at zero degrees Celsius.

0.2 kg of steam at 100 degrees Celsius.

What will the final temperature be?

Using the latent heat of fusion, the latent heat of vaporization, and the specific heat. All of water.

How to calculate the weight, given a mass

Newton’s Second Law states that

F = m a

(Vectors in bold)

Weight = gravitational force (units of Newtons in SI units)

F = m g

g being the acceleration due to gravity.

On Earth, g ~ -9.8 m/s^2

Changes in weight

But that acceleration will change depending on position on the Earth and altitude and will also change on the moon, in space, and in other places.

You can find the acceleration due to gravity by dividing the gravitational force by the mass.

There is an acceleration due to gravity whenever there are two masses, they can be a person sized mass and a planet sized mass, two smaller masses, or any combination of two masses.

Therefore the weight is less or more depending on where it is.

There is less gravity on the moon, so the weight is less there (for the same mass) compared to on Earth.

Let’s say on a bigger planet ‘X’, the mass of the planet is more than Earth. Therefore the acceleration due to gravity is greater and weight would be greater (for the same mass) compared to Earth.

If there are no other masses nearby, in space for instance, things are weightless.

You can use the Law of Gravitation for various situations.

Here’s a diagram

weight given mass

Physics of Speeding Tickets & Skidmarks

If you know the length of a car’s tires skidmarks and the coefficient of friction, you can figure out the starting velocity.

Tutoring Physics – Conversion of Energy, Kinetic Energy into Work Done by Friction

We started by looking at some problems involving conservation of energy and conversion of energy between different types.

The problem we went through a few times involved a car stopping using the brakes and how kinetic energy was converted to heat by the mechanism of friction.

We looked at the units of joules and how equations with work, gravitational potential energy, elastic potential energy, kinetic energy, etc all have the same units.

We also used the equation to derive the units of a spring constant.

Units of Electric Charge

The SI unit of charge is the Coulomb.

Both a proton and an electron have a charge of

1.60217662 × 10-19 coulombs

With a proton having a positive charge with this magnitude and an electron having a negative charge of this magnitude.

An Amphere-Hour is 3600 multiplied by one Coulomb.

Let me know if you have questions about the units of electric charge.

Relation Between Power and Energy (Physics)


There are many forms of energy. Various types of potential energy, kinetic energy, etc.

Energy can be converted between different forms.




Let’s start with a different example though, to understand the relation between power and energy.

Distance and velocity.

Distance is described in units of meters and velocity is described in units of meters per second.

So the difference between distance and velocity is that velocity is divided by time.

With power and energy, power is units of energy divided by time. The same difference as distance and velocity.

The units of power are watts, the units of energy are joules. A watt is one joule divided by one second.

 

FAQ

What is the difference between energy and power?

-Power is energy divided by time. Often units of J/s (joules/second). These are known as Watts. 1 W = 1 J/s

When calculating the amount of electrical energy, you multiply electrical power times what?

-You multiply the power by the time (be aware of the right units for the situation) to get energy

What are the differences between energy and electricity?

-There are many types of energy, the electrical energy from an electric potential is one type of energy.

What does power measure?

-Power measures energy per time. So joules per second is one expression of power. A kilowatt is 1,000 watts.

What is the equation to calculate power?

-That depends on the situation.

What is the difference between watts and kilowatts?

-A kilowatt is 1,000 watts, much like a kilometer is 1,000 meters.

What is the relationship between power and energy and time?

-If you multiply power by time, you get energy. If you divide energy by time, you get power.

P = E/t

You can rearrange that equation in a few ways.