## Mouse Trap Vehicle: Analyzing Motion

**10, 2012**

Earth shattering secrets for building record setting and winning mousetrap cars and racers. Here you will find all the latest and greatest untold construction secrets so you can build your very own mousetrap vehicle.

#### Purpose

To analyze the motion of a mousetrap powered vehicle over 5 meters.

#### Equipment Needed

- Ticker Timer
- Ticker Tape
- Meter Stick

#### Discussion

In this experiment you will collect data from your mousetrap car using a ticker timer. A ticker timer is a device that makes marks on a ticker tape at equal intervals of time. A long piece of ticker tape will be attached to the back of your mousetrap vehicle. As your vehicle is in motion the ticker timer will leave a series of marks on the tape that is attached to your vehicle. Because the time between each mark is the same, a variety of variables can be measured and calculated from the position of each mark. I recommend analyzing the motion of your car over a five meter distance. After your vehicle has made its run, you will be measuring the distance from the first mark to each of the following marks. Velocity is the rate at which your vehicle is covering distance. The greater the rate, the more distance that is being covered per time. The average velocity is the travel distance divided by the travel time. The actual velocity at each mark is calculated from the average velocity by using Formula #2 from the list of formulas. Acceleration is the rate at which your vehicle is changing velocity. In order to find the acceleration you will have to first find the change in velocity between each point using Formula #3. By dividing the change in velocity for each interval, you will calculate the acceleration between each mark (Formula #4).

**ticker timer**: this is the PASCO ticker timer.

v = Δd / Δt

**formula 1**: work [w] is defined in the mathematical terms as a force [f] applied through a distance [d]. This equation is only good for a constant force. Work is measured in joules, force in newtons, and distance in meters.

a = Δv / Δt

**formula 2**: work [w] is defined in the mathematical terms as a force [f] applied through a distance [d]. This equation is only good for a constant force. Work is measured in joules, force in newtons, and distance in meters.

### Step 1:

measure and set-up a 5-meter course in a hallway. Measure 5-meters of ticker timer tape.

### Step 2:

Select or determine the frequency of the ticker timer. The frequency of the ticker tape determines the time between each mark. If the frequency is 10Hz, the time between marks is 0.1s. If the frequency is 60Hz, the time between marks is 1/60 s. Record this frequency in your data table under time.

### Step 3:

Label one end of the tape as the front. Thread the ticker tape through the timer and attach the front of the tape to the rear of the car using a small piece of tape. Position the tape such that the tape does not get tangled with your vehicle s operations during the timing.

**the assembly**: labe the front of the ticker tape and then attach to the mousetrap car.

### Step 4:

Place your vehicle at the start line. Line up the ticker timer directly behind the vehicle tape. Straighten the ticker tape behind the timer so that is passes through the timer without binding. Turn the ticker timer on and then release the vehicle. Remove the tape from the vehicle after the run.

**the assembly**: attach the ticker tape to the rear of the vehicle and then place at the start line. Turn the ticker tape on and release the mousetrap racer allowing the ticker tape to be pull through the timer by the racer.

### Step 5:

From the front of the ticker tape, darken each mark and label as follows: t_{0}, t_{1}, t_{2}, t_{3},...t_{n}.

**ticker tape**: lable each dot on the ticker tape .

### Step 6:

Design a data table to record the following: total time (t), change in time (Δt), total distance (d), change in distance (Δd), average velocity (v), and average acceleration (a).

**data table**: This is a sample data table for step #6.

### Step 7:

Measure the distance between the first mark (t_{0}) and the second mark (t_{1}), record this distance as (Δd_{0,1} ). Measure the distance between the second mark (t_{1}) to the third mark (t_{2}) and record this as the distance between marks (Δd_{1,2} ). Measure the distance between each of the following marks and record as the distance between marks (Δd_{2,3}, Δd_{3,4}, Δd_{4,5} ...). Use the change in distance between each point to figure and calculate the total distance at each marking and record as (d_{1}, d_{2}, d_{3},...,d_{n}. Also record the total time and the change in time between each point in the data table. The change in time should always be the same depending on your ticker timer.

### Step 8:

Add the change in distance between each point and record the total distance for each point from mark (t_{0}).

### Step 9:

Find the average velocity at each mark (t_{n}). Because we want to find the velocity at each mark we need to use a point before and then a point after each mark; for example, in order to find the velocity at (t_{1}) we need to use (t_{0}) and (t_{2}) in order to find that average between the two or at (t_{1}). Follow this technique until all but the last point have been figured. Note: (t_{0}) and (d_{0}) equal 0.

v_{1} = (d_{2} - d_{0}) / (t_{2} - t_{0})

v_{2} = (d_{3} - d_{1}) / (t_{3} - t_{1})

v_{3} = (d_{4} - d_{2}) / (t_{4} - t_{2})

•

•

•

### Step 10:

Find the average acceleration at each mark using the same technique as performed above. Use the information from the mark before and after each mark in order to find the average at each mark. Note: (t_{0}) and (v_{0}) equal 0.

a_{1} = (v_{2} - v_{0}) / (t_{2} - t_{0})

a_{2} = (v_{3} - v_{1}) / (t_{3} - t_{1})

a_{3} = (v_{4} - v_{2}) / (t_{4} - t_{2})

•

•

•

#### Graphing the results

You will now graph your data in order to learn from your results. In each of the following graphs attempt to draw a "best fit" line. If data is widely scattered do not attempt to connect each dot but instead draw the best line you can that represents the shape of the dots. If you have access to a computer you can use a spread sheet like Microsoft Exel to plot your data.

1. Graph Total Distance on the vertical axis and Total Time on the horizontal.

2. Graph Velocity Final at each point on the vertical axis and Total Time on the horizontal.

3. Graph Acceleration on the vertical axis and Total Time on the horizontal.

#### Analysis

1. Identify the time intervals where your vehicle had the maximum positive and negative acceleration. Where did your vehicle have the most constant acceleration?

2. What was the vehicle's maximum speed over the timing distance and at what point did this occur?

3. How far was your vehicle pulled by the string? From the graph is it possible to determine when the string was no longer pulling the vehicle? Explain.

4. Compare your performance to the performance of other vehicles in the class and discuss how yours relates.

*Can't find what you're looking for? Ask Doc Fizzix »