Author Archives: Todd Helmenstine

About Todd Helmenstine

Todd Helmenstine is the physicist/mathematician who creates most of the images and PDF files found on sciencenotes.org. Nearly all of the graphics are created in Adobe Illustrator, Fireworks and Photoshop. Todd also writes many of the example problems and general news articles found on the site.

Impulse and Momentum – Physics Example Problem

Desktop Momentum Balls Toy

This model of a common desktop toy shows the forces acting on the raised ball. The principles of impulse and momentum show how the momentum is transferred to each ball and the process repeats.

Impulse and momentum are physical concepts that are easily seen from Newton’s Laws of Motion.

Start with this equation of motion for constant acceleration.

v = v0 + at

where
v = velocity
v0 = initial velocity
a = acceleration
t = time

If you rearrange the equation, you get

v – v0 = at

Newton’s second law deals with with force.

F = ma

where
F = force
m = mass
a = acceleration

solve this for a and get

a = F/m

Stick this into the velocity equation and get

v – v0 = (F/m)t

Multiply both sides by m

mv – mv0 = Ft

The left side of the equation deals with momentum (often denoted by a lower-case p) and the right side is impulse (often denoted by an upper-case letter J).

Mass times velocity is known as momentum and force applied over time is called impulse.

Impulse and Momentum Example Problem

Question: A 50 kg mass is sitting on a frictionless surface. An unknown constant force pushes the mass for 2 seconds until the mass reaches a velocity of 3 m/s.

a) What is the initial momentum of the mass?
b) What is the final momentum of the mass?
c) What was the force acting on the mass?
d) What was the impulse acting on the mass?

Impulse and Momentum Example Problem

Part a) What is the initial momentum?

Momentum is mass times velocity. Since the mass is at rest, the initial velocity is 0 m/s.

momentum = m⋅v = (50 kg)⋅(0 m/s) = 0 kg⋅m/s

Part b) What is the final momentum?

After the force is finished acting on the mass, the velocity is 3 m/s.

momentum = m⋅v = (50 kg)⋅(3 m/s) = 150 kg⋅m/s

Part c) What was the force acting on the mass?

mv – mv0 = Ft

From parts a and b, we know mv0 = 0 kg⋅m/s and mv = 150 kg⋅m/s.

150 kg⋅m/s – 0 kg⋅m/s = Ft
150 kg⋅m/s = Ft

Since the force was in effect over 3 seconds, t = 3 s.

150 kg⋅m/s = F ⋅ 3s
F = (150 kg⋅m/s) / 3 s
F = 50 kg⋅m/s2

Unit Fact: kg⋅m/s2 can be denoted by the derived SI unit Newton (symbol N)

F = 50 N

Part d) What was the impulse acting on the mass?

The impulse is the force multiplied by the time passed. It is also equal to the change in momentum over the same time period.

Ft = 50 N ⋅ 3 s
Ft = 150 Ns or 150 kg⋅m/s

The impulse was 150 kg⋅m/s.

These problems are relatively simple as long as you keep your units straight. Impulse and momentum should have the same units: mass⋅velocity or force⋅time. Check your units when you check your answer.

Another possible way to cause errors is to confuse your vector directions. Velocity and Force are both vector quantities. In this example, the mass was pushed in the direction of the final velocity. If another force pushed in the opposite direction to slow down the mass, the force would have a negative value compared to the velocity vector.

If you found this helpful, check out other Physics Example Problems.

Neon Rainbow Periodic Table Wallpaper

This rainbow periodic table wallpaper is a colorful addition to our collection of wallpapers.

Neon Rainbow Periodic Table WallpaperThe periodic table contains each element’s number, symbol, name, and atomic mass. It also includes the four new elements: nihonium (113), moscovium (115), tennessine (117), and oganesson (118).

Thiswallpaper is 5760 x 3240 pixels and can be scaled down to look great on any HD device. Click the image to view the full-sized image, or download a copy directly.

We’ve partnered with Redbubble to make posters of many of our periodic tables. This one is no exception. Check it out!  They’ve even got t-shirts, pillows, and coffee cups,

Periodic Table For Kids With 118 Elements

These two “periodic table for kids” tables are simplified tables containing each element’s atomic number, symbol, name and atomic mass rounded to two decimal places. These two tables include the four new elements: nihonium (113), moscovium (115), tennessine (117), and oganesson (118).

Color Periodic Table for Kids

Color Periodic Table For Kids - 2017 EditionThis first table is a color version where the colors correspond to the different element groups.

For easier printing, a PDF is available. The table is optimized to fit on a single 8½ x 11″ sheet of paper.

Black and White Periodic Table for Kids

Printable Periodic Table For Kids - 2017 EditionThis table is better for those without access to color printers or wishes to leave coloring to the student.

As with the color version, a PDF is available for downloading and printing.

If you enjoy these periodic tables, check out our many other periodic tables.

Periodic Table In Black and White Wallpaper

This wallpaper periodic table in black and white is a simple and clean design.

Periodic table in black and whiteEach element is represented by its atomic number, symbol, name, and atomic mass. This periodic table also includes the four new Period 7 elements: nihonium, moscovium, tennessine, and oganesson.

This wallpaper is optimized to look great on a 4K display at 3840 x 2160 pixels but looks great on HD monitors and devices when scaled down. Click the image or download to view the full-sized image. If you’d like to print a copy, download the PDF and set your options to “Fit” and “Landscape” for best results.

Periodic Table In White and BlackThis periodic table is the same table, just reversed. The text and borders are white and the background is black. Click the image or download directly.

Neon Periodic Table With 118 Elements Wallpaper

If you look closely, this neon periodic table wallpaper shows each element surrounded by colored neon bulbs.

Neon Periodic Table - 2017 Edition (118 Elements)The different colors correspond to the different element groups. Match the group to the color using the legend along the bottom. Each element is represented by its number, symbol, name, and atomic mass. This table also includes the four new Period 7 elements: nihonium, moscovium, tennessine, and oganesson.

This wallpaper is optimized to look great on a 4K display at 3840 x 2160 pixels but looks great on HD monitors and devices when scaled down. Click the image or download to view the full-sized image. If you’d like to print a copy, download the PDF and set your options to “Fit” and “Landscape” for best results.

Some folks find a white background a little hard on the eyes for their monitors. This periodic table is the same table with a black background and high-contrast white text. Click the image or download directly.

Neon Periodic Table With Black Background - 2017 Edition

Large Print Periodic Table

No time for fine print. This large print periodic table will help you with your eye strain.

Color Large Print Periodic Table

Color Large Print Periodic TableThis color periodic table contains the usual element numbers, symbols, element names, and atomic masses, but has the added bonus of larger type. This periodic table includes all 118 elements known as of 2017.

The element names are as large as I could consistently make them. I chose to make the names a uniform font size with the exception of the really long ones (rutherfordium, darmstadtium, roentgenium, and praseodymium). The rest of the information is much easier to read than the usual printable periodic table.

To print, download the PDF and choose either “Fit” or “Shrink oversized pages” under Page Sizing and Handling in the print options. Remember to choose Landscape for your orientation to use more space on the paper.

Black and White Large Print Periodic Table

This is basically the same table, only monochromatic!

Large Print Periodic TableDownload this PDF if you don’t have access to a color printer, or just want to save your color inks or toners. Choose the same options as the color periodic table to print on a single sheet of paper.

If you like this table, check out our other printable periodic tables.

Neon Hexagon Periodic Table Wallpapers – HD Periodic Table Wallpapers

These neon hexagon periodic table wallpapers are made up of hexagons honeycombed together for an interesting and different layout. The text contains each element’s number, symbol, name, and atomic mass.

You may remember these periodic tables as one of our first periodic table wallpaper styles. Since then, there has been the addition of four new elements: 113 (nihonium, Nh), 115 (moscovium, Mc), 117 (tennessine, Ts), and 118 (oganesson, Og). This brings the total number of elements to 118 named elements and completes the Period 7 elements.

Since the table does not look like the usual periodic table, you will have to oscillate right then left and back right again as you move down a column. Horizontal movement works the same as before.

These periodic tables are all suitable for 1920×1080 HD monitors and devices. To download your favorite, just click the image or download the file from the title above each image.

Red Neon Hexagon Periodic Table

Red Neon Honeycomb Periodic Table - 2017 Edition

Red on black for a vaguely sinister feeling periodic table.

Light Blue Neon Hexagon Periodic Table

Light Blue Neon Honeycomb Periodic Table - 2017 Edition

Glowing highlighter blue text is kind of relaxing in its own way.

Green Neon Hexagon Periodic Table

Green Neon Honeycomb Periodic Table

The hexagons of this periodic table have a green radioactive glow.

Aqua Neon Hexagon Periodic Table

Aqua Neon Honeycomb Periodic Table - 2017 Edition

Not quite green, not quite blue. Go for an “Under the Sea” theme with this periodic table.

Blue Neon Hexagon Periodic Table

blue neon hexagon periodic table

Feeling blue? Let these blue hexagons take the blues away!

Purple Neon Hexagon Periodic Table

Purple Neon Honeycomb Periodic Table - 2017 Edition

Purple is the color of royalty. Feel regal with this purple neon periodic table.

Yellow Neon Hexagon Periodic Table

Yellow Neon Honeycomb Periodic Table - 2017 Edition

A yellow theme to warn of danger or marking construction areas. I say this periodic table is dangerous.

Orange Neon Hexagon Periodic Table

Orange Neon Honeycomb Periodic Table - 2017 Edition

Orange text and hexagons put me in mind of pumpkins and Halloween! Trick or Treat yourself to this orange hexagon periodic table.

Pink Neon Hexagon Periodic Table

Pink Neon Honeycomb Periodic Table - 2017 Edition

Pink hexagons make a simply awesome color for a high contrast desktop wallpaper. Go Pink!

Gold Neon Hexagon Periodic Table

gold neon hexagon periodic table

This is the gold standard of neon hexagon periodic tables!

White Neon Hexagon Periodic Table

White Neon Honeycomb Periodic Table - 2017 Edition

White on black for that chalkboard periodic table you’ve always wanted.

Inverted Hexagon Periodic Table

Inverted Honeycomb Periodic Table - 2017 Edition

This periodic table looks kind of spooky and skeletal!

If you like these periodic table wallpapers, check out our other fun high-quality wallpapers.