# Accelerated Motion

## Materials:

• lab sheet and writing utensil
• calculator
• spreadsheet and graphing software
• string
• 20 g mass with hook
• “frictionless” track + cart
• motion sensor  + computer with sensor control and analysis software (self-tracking motion cart optional).

## Preparation

Before we begin creating and testing a hypothesis regarding forces and motion, we need to familiarize ourselves with basic motion concepts and the equipment we will use to measure motion.

First set up the motion sensor and analysis program so that it displays the position, velocity, and acceleration vs. time graphs of your motion as you move in front of the sensor.

Next, create each of the following graphs by moving in front of the motion sensor. Have your instructor sign off on each graph as you progress.

Outcome 7-3

### Constant Position

Create a constant position graph. Instructor signature:____________

Describe how you had to move to create this graph.

Describe the velocity and acceleration graphs created by your motion.

### Constant Velocity

Create a constant velocity graph. Instructor signature:____________

Describe how you had to move to create this graph.

Describe the position and acceleration graphs created by your motion.

### Constant Acceleration

Create a constant acceleration graph. Instructor signature:____________

Describe how you had to move to create this graph.

Describe the position and velocity graphs created by your motion.

## Accelerated Motion

Outcome 7-4

Now we will use the cart and track to test a hypothesis about how position, velocity, acceleration and net force are related. Setup the cart and track and motion sensor (or the self-tracking cart) to measure the position, velocity, and acceleration of the cart as it moves down the track.

### Observation

So far we have been working only in situations when all forces were balanced, so the net force was zero.

### Questions

What happens when there us only one unbalanced force so the net force is not zero?

### Search Existing Knowledge

Search for answers to the previous questions. Write down what you find and be sure to cite your sources.

### Qualitative Hypotheses

Provide a qualitative hypothesis about what will happen when the net force on an object is not zero.

### Test

We will start by applying a single unbalanced force to an object. The object will be a cart. The cart will run on a smooth track to minimize friction. We will use a fan attached to the cart to cause a constant force on the cart. Without the fan running, the cart should stay in static equilibrium. Place the cart on the track and let go. Does the cart start rolling? If so, then there must have been an unbalanced force on the cart, even though the fan was off, so the track is probably not level. Level your track.

### Analyze

Now turn on the fan and measure the velocity and acceleration of the cart.

What happens to the cart when the fan is running? Was the velocity constant or changing?

If the velocity was changing, record the acceleration here: _________

Record the standard deviation in the acceleration here:_____________

### Conclusion

Does the result of your test agree with your qualitative hypothesis? Explain.

## Verification of Newton’s Second Law

Outcome 7-4

During your search of existing knowledge you likely came across Newton’s Second Law, which tells us how net force, mass, and motion are related. Look up and write down Newton’s Second Law:

### Test

Newton’s Second Law has been well established, but to help us understand the law we want to re-test Newton’s Second Law.

Measure the combined mass of the cart and fan and record here:__________

Use your previously measured acceleration, the cart mass, and Newton’s 2nd Law to calculate the expected force provided by your fan:

Repeat the acceleration measurement for four additional cart masses (change the cart mass by adding accessory masses). Record all results, including standard deviations for the accelerations, in a chart below. Leave an extra empty column at the end.

### Analyze

Use the fan force you calculated in the first trial to calculate what the accelerations should have been for each of the four additional trials. You may use a spreadsheet. Record your results in the empty column of the previous chart.

Did Newton’s Second Law allow you to correctly predict the accelerations of your cart within the uncertainty in the acceleration measurement? Explain.

#### Double Check Assumptions

Let’s double check our assumption that friction (or other forces) are  not affecting our results. If our assumption that air resistance is negligible is valid, then these forces should be much smaller than the force provided by the fan. With the fan off, give the cart a gentle push and measuring the acceleration as the cart slows down due to air resistance and friction. Record the average acceleration of the cart during slow-down here:

Use the mass of the cart and Newton’s Second Law to calculate the force on the cart due to air resistance and friction.

### Conclusion

Do you think that friction and air resistance had a large effect on your test of Newton’s Second Law? Explain by comparing the size of those forces to the fan force.

Did your test of Newton’s Second Law provide evidence in support of Newton’s Second Law? Whether the answer is yes, no, or inconclusive, be sure to explain how you arrived at that decision.

## License

Body Physics: Motion to Metabolism Copyright © by Lawrence Davis is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.