## Mouse Trap Vehicle: Starting Energy

**05, 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 calculate the starting potential energy and to find the spring coefficient.

#### Equipment Needed

- Spring Scale or a Computer Force Probe
- Doc Fizzix's Tension Wheel (recommended but not needed)

#### Discussion

Energy has the ability to do work. Your mousetrap car's performance will depend directly on the strength of your mousetrap's spring. The stored energy of your spring in the fully wound-up position is called potential energy. The amount of stored potential energy is the same as the work that was required to wind the spring. The force required to wind the spring times the distance the force was applied is equal to the work that was done on the spring (Formula #1). Because the force required to wind the spring changes and depends on how much the spring is wound, you will have to find the average force between a series of points and then calculate the work done between those marks. The total work (or the stored potential energy) is equal to all the changes of energy between all the points added together. In order to measure the winding force you have to use a spring scale attached to a lever. The lever is lifted and the force is measured every 5 or 10 degrees. The scale has to be held such that the string attached to the lever arm is perpendicular. A problem with this method is that as the spring scale is held in different positions it becomes inaccurate. The spring scale cannot change from the position at which it was zeroed. For this reason I recommend using a tension wheel. A tension wheel allows the spring scale to remain in one position, producing more accurate results and it is easier to use.

**travel distance**: measure the maximum travel distance.

The distance that the average force was applied is equal to the angle of the measurement in radians times the length of the measuring lever arm. If you are using a tension wheel, then the radius of the wheel is the measuring lever arm (Formula #2). Formula #3 allows you to convert from degrees to radians.

For a spring that is stretched or compressed longitudinally, Hooke's Law applies and says that the force is equal to the spring constant times the stretching or compressing displacement (Formula #4). But a mousetrap spring does not stretch longitudinally. A mouse trap spring is a torsion spring and winds up. For this type of spring a different formula is needed (Formula #5). It is a torque that must be applied to the spring to wind it and the displacement is measured in radians (Formula #5). The units associated with the spring constant become Newtons * Meters/ Radians. For a spring that compresses or stretches in a linear direction, the total potential energy is one half the spring constant times the displacement squared (Formula #6). For a torsion spring the displacement is substituted by the angle in radians (Formula #7).

W = F × d

**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.

d = θr

**formula 2**: the linear travel distance for a wheel [d] it equal to the angle of turn in radians [θ] times the radius [r] of the wheel.

θ = degrees × Π/ 180

**formula 3**: the linear travel distance for a wheel [d] it equal to the angle of turn in radians [θ] times the radius [r] of the wheel.

F = -kx

**formula 4**: Hooke's law says that the force of a spring [F] is equal to the spring constant [k] times the displacement of the spring [x].

τ = -kθ

**formula 5**: the torque of a torsional spring is equal to the spring constant [k] times the angle of twist [θ]. Torque is measured in newtons times meters, the spring constant is measured in newtons per meter, and the angle of the twist is measured in radians.

PE = (1/2) × kx^{2}

**potential energy 6**: the potential energy [pe] of a stretched/compressed spring is equal to one-half the spring constant [k] times the distance [x] stretched/compressed squared. Potential energy is measured in joules, the spring constant in newtons per meter, and the distance in meters.

PE = (1/2) × kθ^{2}

**potential energy 7**: the potential energy [pe] of a torsional spring is equal to one-half the spring constant [k] times the angle of the twist [θ]. the potential energy is measured in joules, the spring constant is measured in newtons per meter, and the angle of the twist is measured in radians.

**travel distance**: measure the maximum travel distance.

**travel distance**: measure the maximum travel distance.

### Step 1:

Attach the Doc Fizzix Torsion Wheel to your mouse trap's spring as show in the picture. Start by removing the mouse trap's spring and then transfer the spring to a temporary mouse trap base for testing purposes. Follow the steps bellow for assembly.

**the assembly**: the doc fizzix torsion wheel attached to a mouse trap spring.

**how to assemble part 1**: hold the mouse trap spring flat on the base as pictured and then slide the torsion wheel through the mouse trap loops and spring.

**how to assemble part 2**: make sure the torsion wheel's bar slides under the mouse trap's spring as pictured.

### Step 2:

Attach the mouse trap base to the edge of a table using a C-clamp as pictured.

**the assembly**: attach the mousetrap and set-up to the edge of a table using a C-clamp as pictured.

### Step 3:

Using a force probe or spring scale attached to the Torsion Wheel's string, pull down on the force scale until the 0 degree mark is lined up with the base of the mouse trap as pictured and record the force as the starting tension (force).

starting tension (F_{0}) = _____ N

**the starting tension**: pull down on the force scale until the 0 degree mark is lined-up with the mouse trap's base, record the force as the starting tension.

### Step 4:

Continue to pull down with the force probe recording the pulling force at every 5 or 10 degree increments. Record the pulling force at each measuring point in a table.

tension at 5 degrees (F_{1})= _____ N

tension at 10 degrees (F_{2})= _____ N

tension at 15 degrees (F_{3})= _____ N

tension at 20 degrees (F_{4})= _____ N

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tension at 180 degrees (F_{n})= _____ N

### Step 5:

Calculate the change in radians for each angle and record them in the data table. If each measurement was made at the same increment (e.g., 5, 10, 15, 20 ...) you can use the same change in radians for all angles. Use the following method to calculate the change in radians:

Δθ_{1} = (degree_{1} - degree_{0}) × Π/ 180

Δθ_{2} = (degree_{2} - degree_{1}) × Π/ 180

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### Step 5:

Calculate the change in displacement, also known as the arc length, for each angle using the following formula. If each measurement was made at the same increment, (e.g. 5, 10, 15, 20 ...) you can use the same arc length (displacement) for all angles. Note: the radius is printed on the Torsion Wheel, use this value for the radius.

Δd_{1} = Δθ_{1}r

Δd_{2} = Δθ_{2}r

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**torsion wheel radius**: the radius is printed on the Torsion Wheel, use this value for the radius.

### Step 6:

Calculate the change in potential energy between each point using the following method. Multiply the average force between the starting and ending points with the change in distance.

ΔPE_{0,1} = ((F_{0} + F_{1}) / 2) Δd_{1}

ΔPE_{1,2} = ((F_{1} + F_{2}) / 2) Δd_{1}

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### Step 7:

Add all the changes in potential energy in order to find the total starting energy.

PE_{total} = PE_{0,1} + PE_{1,2} + PE_{2,3} + • • •

### Step 6:

Calculate the spring constant using the formula bellow. Use the starting and ending pulling forces and the TOTAL change in radians. In most cases, the total number of radians is equal to 180 degrees or Π. Note: the radius is printed on the Torsion Wheel, use this value for the radius.

τ = -kθ

k = ((F_{n} - F_{0})r) / θ_{total}

#### Graphing the results

In each of the following graphs attempt to draw the best fit lines. If data is widely scattered do not attempt to connect each dot but instead draw the best 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 **Pulling Force** on the vertical axis and the **Displacement** on the horizontal axis.

2. Graph **Torque** on the vertical axis and **Angle in Radians** on the horizontal.

#### Analysis

1. The slope from your graph of **torque vs. angle** represents the spring constant. Does the slope change or remain constant? Do you have an ideal spring that follows Hooke's Law?

2. What does the slope of the line from each of your graphs tell you about the strength of your spring compared to other students' graphs?

3. Calculate the area under all parts of the best-fit line from the graph of **torque vs. angle**. This number represents the potential energy you are starting with. The larger the number, the more energy you have to do work. This number should be close to the total potential energy calculated from your data table. How does the slope compare to the number in the data table?

4. How does your potential energy compare to other students potential energy in your class? Discuss.

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