## Introduction: Physics Labs at Home!

Where I live, school was suspended in March, and our classes were moved online. That was okay and everything, but when it came to science, all the labs went out the door. (Virtual labs just aren't the same, if that's what you're thinking.) So, I decided to design a few physics labs myself, and for those students who missed out on the best part of physics, I hope this Instructables assuages some of your disappointment!

This lab is probably meant for grade 11 physics students, and focuses on kinematics and dynamics. We'll be exploring forces, acceleration, friction, and all that good stuff!

## Supplies

• 3D printer

For lab #1 (acceleration on a slope):

• 3D printed dynamics cart
• device with stopwatch camera app (such as this one)
• smartphone with Google Science Journal app (optional)
• a plank of wood or something around 1 meters long
• books to prop up the plank of wood
• protractor
• digital kitchen scale

For lab #2 (acceleration with a mass):

• 3D printed dynamics cart
• 3D printed pulley
• a device with a stopwatch camera app
• smartphone with Science Journal app (optional)
• a table
• string
• digital kitchen scale
• plastic water bottle (that you are willing to sacrifice to dents and bruises)
• tape measure

## Step 1: 3D Printing the Dynamics Cart

I designed a dynamics cart on Tinkercad to hold a smartphone (it's adjustable for size), and I've included the stl files for you to print. If you would like to make adjustments or design your own, click on the image above to view the design! A note for those who would like to do some tinkering: for a tightly fitting sliding parts, I used a gap of 0.15 mm on each side; for loosely fitting parts, I used a gap of 0.4 mm on each side.

For printing, I recommend using at least 50% infill density, and the use of supports. If your material warps easily, you probably should not print the axes. Use wooden skewers instead.

Once it is done printing, you will have to remove all the supports, especially inside the holes. Put the axes through the holes (they should spin freely), and stick the wheels on at the ends of the axes (this should be a tight fit). Depending on your 3D printer and/or whether you use skewers, you may have to do some sanding to make everything fit. The two parts of the cart should slide together tightly, but still be adjustable. If it is too tight, do some sanding; if it is too loose, wrap some tape around the inner sliding component.

## Step 2: 3D Print the Pulley

Attached are the files for the pulley. The same printing instructions apply, and, again, you may replace the axis with a skewer.

To assemble, position the spool between the arms of the stand, and insert the axis at the desired height. The axis should fit snugly into the holes, with the spool spinning freely.

## Step 3: Lab #1: Acceleration on a Slope

Before we start:

When an object is sliding down a slope, there are several forces acting on it. The force of gravity is directly downwards (as always), the normal force is upwards and perpendicular to the plane between the object and the slope, and the force of friction is opposite to the direction of motion. Notice that the force downwards and parallel to the slope is a vector component of the force of gravity (the other component is balanced by the normal force). This force causes the cart to accelerate down the slope (hopefully there isn't too much friction), and the magnitude of the force is dependent on the angle of the slope! We will be demonstrating this in the following lab. Also, don't forget Newton's second law: force = mass x acceleration!

## Step 4: Lab #1: Acceleration on a Slope

First of all, make a hypothesis! Will acceleration increase with angle? Will it be a linear relationship or otherwise?

Procedure:

Note: I designed the cart to be used with the accelerometer in Science Journal. However, when I was testing out the lab, I found the app was not very accurate, possibly because I am using an old version. If you would like to give it a try, follow the instructions below.

1. Make a data table like the one in the photo.
2. Open the science journal app, click "+" to start a new experiment, and click on linear accelerometer.
3. Fasten your phone to the dynamics cart.
4. Prop the plank at a 10 degree angle to the floor with some books. Add a few pillows at the bottom end!
5. Position the cart at the top of the slope, start recording the accelerometer, and release the cart. Turn off the recording after the cart reaches the bottom.
6. Crop the recording to the duration that the cart was going down the slope, and record down the average acceleration.
7. Repeat for a total of three trials.
8. Repeat for angles 20, 30, and 40 degrees.

Using the video stopwatch yielded better results for me. Here are instructions for the video stopwatch:

1. Make a data table.
2. Prop the plank at a 10 degree angle to the floor with some books. Add a few pillows at the bottom end!
3. Place a tape measure along the plank of wood.
4. Place a device with a camera in a position that captures the entire track. Start the video stopwatch.
5. Position the cart at the top of the slope and release! Stop the recording after the cart reaches the bottom
6. Repeat for trials two and three.
7. Repeat for angles 20, 30, and 40 degrees.

I will explain how to get your data for this method in the next step.

## Step 5: Dealing With Your Data

The video stopwatch method requires a few calculations to get your data.

Calculating initial velocity:

• Find a frame right after the release of the cart and write down the time as well as the cart's position along the tape measure.
• Scroll forward one frame and write down the time and the new position.
• To find the instantaneous(ish) velocity: velocity = displacement / change in time
• So, velocity = (final position - initial position)/(final time - initial time). This best represents the acceleration at the time in the middle of the time interval, so time = (initial time + final time)/2.

Calculating final velocity:

• Repeat the steps above for a frame near the end of the video.

Calculating average acceleration: acceleration = change in velocity / change in time

• So, acceleration = (final velocity - initial velocity)/(final time - initial time).

An example is provided in the photo. Note that plotting velocity over time and using a best fit line to find the acceleration can be more accurate, but it is very tedious.

## Step 6: Lab #1: Acceleration on a Slope

Analysis:

So... what do you notice? Plot the angle on the x-axis, and the average acceleration on the y-axis to see if your hypothesis is right. Is it a linear relationship, aka a straight line? (probably not)

This time, try plotting the acceleration vs sinθ. Straighter? Let's take a look at why:

First, let's assume that friction is negligible (because it makes things very complicated), and hopefully the cart doesn't have too much friction! The force down the slope (Fx) is related to Fg (the force due to gravity):

sinθ = Fx/Fg (opposite over hypotenuse)

Fx = Fgsinθ

F = ma, so acceleration a = F/m. Therefore, a = Fx/m = Fgsinθ/m. Since Fg and m are constants for the same mass, you have the relationship that a is proportional to sinθ! (If your graph says otherwise, blame friction.)

Discussion questions:

Use the kitchen scale to find the mass of your cart. Assuming negligible friction, try calculating the theoretical acceleration of the cart at 30 degrees (or any of the other ones, but you can use special triangles with 30 degrees). How much does it differ from your experimental value? Challenge: can you calculate the force of friction?

Conclusion: Yay you learned something! I won't torture you; this isn't a formal lab.

## Step 7: Lab #2: Acceleration With a Mass

Before we begin:

This setup involves the concept of tension, which is a force transmitted by a string (in our case). The mass that we hang over the pulley experiences a downwards force due to gravity, and an upwards tension. According to Newton's third law, the cart experiences tension of the same magnitude, but in the opposite direction. This can be a little hard to see, since the pulley kind of "bends" the force at a 90 degree angle. The force of gravity on the cart is balanced by the normal force, so the net force on the cart is tension minus friction. Since our string is not stretchy, the mass and the cart must experience the same acceleration.

## Step 8: Lab #2: Acceleration With a Mass

Make a hypothesis: How will the acceleration of the cart change when the mass hanging over the edge of the table is increased? (Hmm, all free falling objects have the same acceleration of 9.8 m/s^2 regardless of mass, but what happens when you add a cart?)

Procedure:

Again, you have the choice of using Science Journal:

1. Make a data table.
2. Click on the linear accelerometer function and fasten your phone on the cart.
3. Tape the pulley at the edge of the table.
4. Fill the bottle of water until it is 100 g.
5. Cut a length of string longer than the height of the table. Tie one end to the bottle, and the other to the cart.
6. Put the string over the pulley, and draw the cart back until the bottle is at the top. Start recording, release the cart, CATCH THE CART BEFORE IT FALLS OFF, and stop the recording.
7. Repeat for a total of three trials.
8. Repeat for 200g, 300g, and 400g.

Video Stopwatch directions:

1. Make a data table.
2. Tape the pulley at the edge of the table.
3. Put the tape measure along the length of the table.
4. Fill the bottle of water until it is 100 g.
5. Cut a length of string longer than the height of the table. Tie one end to the bottle, and the other to the cart.
6. Put the string over the pulley, and draw the cart back until the bottle is at the top.
7. Position the stopwatch camera to capture the whole setup. Start recording, release the cart, CATCH THE CART BEFORE IT FALLS OFF, and stop the recording.
8. Repeat for a total of three trials.
9. Repeat for 200g, 300g, and 400g.

## Step 9: Lab #2: Acceleration With a Mass

Data:

The same instruction apply as with the first lab for finding acceleration for both Science Journal and the video stopwatch method. For the stopwatch method, audio is a good indicator for when the bottle hits the floor (take your final velocity before this point).

Analysis:

How does your hypothesis compare with the data?

Can you explain why acceleration increases with mass of the water bottle?

What happens if you change the mass of the cart instead of the hanging mass?

Discussion questions:

Find the mass of your cart. Assuming no friction, can you calculate the theoretical acceleration for a hanging mass of 400g (or any other of your choice)?

Hint: for the mass a = (mg - T)/m, for the cart a = T/M, and these two accelerations are equal to each other. Solve for T to find acceleration!

How does this compare to your experimental value? Challenge: calculate percentage difference between the theoretical value and experimental value.

Conclusion: Thanks for sticking with me, and I hope your brain didn't explode! Hope you had fun!

## Step 10: Want More?!

Oh all right... if you are really that eager! Try designing some of your own labs. You can use the pulley system to find the coefficient of friction between the table and a different materials by increasing mass until the water bottle drags the material across the desk. Or you could print another cart, add some bumpers, and explore momentum in collisions. Or your could melt your cart in the oven as a thermodynamics experiment... (kidding!)