Physics Principles of a Mousetrap Car

Before Christmas Break, a fun project we were assigned was to design and build a mousetrap powered car. To begin with, my partner and I researched some simple mousetrap car designs, that we could build off of to maximize the distance our car could go. We decided that we would use a thin foam board as the body of our car, as it is a lightweight, and easily attainable material. For the wheels of our car, we initially thought that old CDs would be the best option, and for the axles we thought that we should use wooden skewers. Lastly, we were unsure of the best type of string/line to use to power the car, so we decided that we would experiment with different types of string.

The most difficult part to this project, was just getting the car to move. The propulsion of the car had to be solely from the spring of the mousetrap, therefore we had to find a way for the spring to spin the back wheels of the car. To power our car, we attached the mousetrap to the front of the body of our car, with the hammer of the mousetrap being furthest away from the back of the back wheels.  Then we took fishing line, and tied it to the hammer. With the fishing line, we stetted the line to the back end of the car, and tied the line around the  axle of the back wheels, which spin freely, being supported in drinking straws. I also glued a small piece of toothpick to the back axle, so that the string will wind around the axle. So to make the car move, one person has to hold the hammer back to tighten the spring, and the other person has to start winding the slack of the line around the back axle. Then when both people let go, the spring will begin to pull back into its original position, and the spring force will spin the back wheels to make the car move.

http://www.millerandlevine.com/km/evol/DI/Mousetrap.html

We thought that to maximize the distance the car could go, we would need to use large back wheels, so that one turn of the axle, would make the car  go further. In addition, we thought that making the car longer, and attaching the mousetrap further away from the back wheels of the car, would allow more slack in the string to wind around the wheels, and therefore make the car go further.

When I went shopping for supplies, I found different sizes of foam circles, that are usually used for floral arrangements, but would work well as wheels because they are 1 inch thick, which are much more stable than CDs. I also decided to buy 2 different sizes because the back wheels are the only ones that need to be large as the car is powered by the back axle, therefore for the front wheels I decided to buy smaller pieces of foam as it is lighter. As I also mentioned before, I decided to use fishing line because it is strong, yet a little bit stretchy which will allow us to wind the string/wheels as much as possible.

The car eventually looked as seen above. You might notice in the picture, that all four wheels are covered in masking tape. This is to deal with the issue of friction.  We did this to create more grip on the wheels, and to maximize the distance of each spin of the axle. Although a lever arm would have been beneficial to make the car go further, as it increases the pulling  force on the fishing line (which makes the wheels spin more and make the car go further), I decided not to put a lever arm on the hammer of the mousetrap as I found it very difficult to find a material that would be able to stick to the hammer, be stiff enough to withstand the pull from the spring, and be light enough to not throw off the balance of the car.

On the last day of school before winter break, we performed trial runs to see how far our cars could go. I wasn't expecting much, however our car was actually able to travel approximately 8.3 m which is much further than I thought it could go. An observation I made was that our car moved very slowly when it started to move, but actually went fairly far. With regarding power, this shows that our car is not very efficient because it moves so slowly, which means that lots of power is being wasted. One adjustment that I would make would be potentially adding a lever arm, however I need to find the right material to use to make the car run more effectively, and travel a longer distance.

Newton's Law and Momentum Application

Common practice problems we do when dealing with momentum involve car collisions, but not only does this involve physics theoretically, but also explains some safety features on cars. Newton's first law states that an object in motion will stay in motion, and an object at rest will stay at rest unless acted on by an unbalanced force. For cars, this is true as cars will continue moving unless the brake is applied, or it collides with an object. Newton's third law states that for every action, there is an opposite and equal reaction. For example, if a car and a truck collide, they will experience the same magnitude of force, but the driver of the car will be worse off because of Newton's second law, which means that the car experiences a larger acceleration due to the truck having a greater mass (F=ma).

Since we know that momentum is conserved, this means that it can only be transferred from one object to another. The law of conservation of momentum states that in a closed system, the total momentum stays the same. In a car collision, this means that if one car loses x amount of momentum, the other car will gain that same amount, as it is being transferred.

This explains the reason for seat belts in vehicles. Going back to Newton's First Law, and object in motion will stay in motion. This means that when a car hits an object, the car will be acted on by an unbalanced force and stop, however the driver will continue forward. We wear seat belts to hold the driver or passengers back from flying forward. If we don't wear seat belts, a force will act on the person to slow them down, however this force will come from the windshield causing much more damage, and possibly throwing the person out of the car. The seat belt provides a softer, stopping force to minimize the damage in car accidents.

http://hyperphysics.phy-astr.gsu.edu/hbase/imgmec/carcr5.gif

Airbags are placed in cars to reduce the speed of the passenger in a car during a collision. The passenger of the car has momentum because of the passenger's mass and velocity. In order to stop this momentum, another force must act on the passenger. Instead of the passenger hitting the dashboard or windshield of the car, airbags are used to soften the blow and minimize the injuries of the person. The airbag provides a change in momentum, also known as impulse. The more time a force has to act on an object, the less damage to the passenger. 

http://www.carsp.ca/hitech/airbags.jpg

In addition to having airbags and seat belts, car also have crumple zones to reduce the impact of collisions. The front and back ends of cars have what are called crumple zones. These increase the amount of time that the force acts on the car during a collision. With an increased amount of time, the force acts over a longer period of time, which reduces the affects of the force when it reaches the middle of the car, where the passengers are. Crumple zones help minimize the injuries sustained in car collisions. 

http://tristanmac.tripod.com/sitebuildercontent/sitebuilderpictures/crumples.gif

Lastly, another safety feature of a car are the headrests. Not only do headrests provide comfort, but they also prevent neck injuries during collisions. In some collisions, when a car hits another object, or hit the brakes, the car stops moving, but from what we know from Newton's first law, the driver's body will continue moving. In this case, the driver's head could be thrown either forwards or backwards, and once the head is thrown one way, it will naturally be thrown the other way due to the way our neck muscles react. Headrests help prevent neck injuries by providing a softer way to stop the head and neck of a driver. 

http://tristanmac.tripod.com/sitebuildercontent/sitebuilderpictures/headrest.gif

Vector Dynamics Application

Vector dynamics can be applied everywhere we look. Although we learned more about vector dynamics, a large part of this unit was focussing on inclined planes, therefore, a practical application of vector dynamics is skiing. Skiing has always been a sport that I have wanted to do more often. I have had the opportunity to ski on local mountains and have loved the few time I have been able to go! There are many different types of skiing, and all would show good examples of how forces act on an object, whether the person is skiing down a hill, or on a flat surface like cross country skiing.

https://www.inkling.com/read/college-physics-openstax-college-1st/chapter-5/example-5-1

In this diagram, we can see that the skier is on a incline of 25 degrees, and the free-body diagram shows that there is a normal force, (Fn) the force of friction (Ff), and the force of gravity (Fg) acting on the skier. The force of friction would come from the snow under skis. As we have learned in this unit, the force of gravity can be split into 2 components, a parallel component, and a perpendicular component. We separate gravity into components so that the perpendicular component balance Fn, and the parallel component is parallel to the direction the object is moving in, and the force of friction. 

We have already learned that we can find Fg perpendicular by using the formula, mg cos θ. In this situation, θ is 25 degrees because the incline of the surface is 25 degrees. Additionally, Fg parallel= mg sin θ. With these components, we could now find values such as the force of friction, and the acceleration of the skier, depending on the other information given. This type of information can be especially useful if you practice ski jumping, which can be based on how fast you accelerate down the hill, and how far you can jump. 

http://www.saugeentimes.com/Pictures/Misc%20Clip%20Art/Cross%20Country%20Skier.jpg

For a cross country skier, who must move on a relatively flat terrain, the forces acting on them are the normal force (Fn) the force of gravity (Fg), and the force of friction, however friction plays a more prominent role in cross country skiing. If you have looked at cross country skis, you will notice that the skis will not lie completely flat against the snow. This is because a cross country skier, needs both high and low friction forces while skiing. Friction needs to be low when the skier is gliding forward, however it needs to be high when you kick back and grip the snow to move. This arch in the ski allows you to adjust your weight depending on the situation. When you guide the ski forward or are going downhill, your weight on the skis decreases, and the arch ensures that the middle portion of your skis do not make contact with snow, therefore, there is less friction. However when you kick back, your body weight pushes on the ski, and the middle section touches the snow, therefore more friction!

http://sciencenordic.com/physics-cross-country-skiing

Vector Dynamics Reflection

For the second unit of the year, we reviewed and further studied Vector Dynamics. To begin with, we reviewed Newton's Three Laws of Motion:

1. Every object in a state of uniform motion remain in that state unless an external force is applied to it. This is also called the Law of Inertia because inertia is the resistance of an object to change its motion. This means that if an object is moving at a constant speed, it will keep going unless another force act on it. Similarly for object at rest, they will remain at rest until a force acts on it.

http://www.physicsclassroom.com/class/newtlaws/u2l1a.cfm

2. The relationship between an object's mass, its acceleration, and the applied force is F=ma. This allows us to quantitatively calculate dynamics.

3. For every action there is an equal and opposite reaction. This is exemplified when we look at a pulley system. The acceleration of one mass going down is the same as the acceleration of the other mass in the opposite direction.

http://session.masteringphysics.com/problemAsset/1131786/3/Figure_8.47.jpg

Using these principles, we looked at problems applying our knowledge from grade 11 to solve problems. To solve any dynamics problem, we start by drawing a free body diagram, and identifying all the forces acting on the object. From here, we write our force equation, and then can solve for missing values depending on the information given. 

The grade 12 portion of this was looking at forces in 2 dimensions. An example of a type of question would be an object on a ramp. The difference between objects on an inclined plane, and an object on a flat surface would be that the force of gravity (Fg) can be split into a parallel and perpendicular force of gravity, relative to the inclined plane. The components from Fg create a right triangle, where θ of the ramp is equal to the angle of the right triangle.

http://simple.wikipedia.org/wiki/Inclined_plane

If we know the angle of the ramp, Fg parallel can be found using the equation, Fg parallel=mg sin θ, and Fg perpendicular=mg cos θ. Therefore, the normal force (Fn) and Fg perpendicular balance, and Fg parallel is parallel to the ramp. Now that we can find these components, we can solve for various values, for example, the force of friction, or the acceleration of the object, amongst other values. With this concept in mind, we can also solve more complicated problems, incorporating pulleys on inclined planes.

http://www.sparknotes.com/testprep/books/sat2/physics/chapter8section3.rhtml

The biggest difficulty I had with this unit was learning to think of Fg as 2 components, and then using these components to find which forces balance and which attribute to the net force. To overcome this, it was really important for me to draw a proper free body diagram, to correctly label all the forces acting on an object, and have all my arrows going in the appropriate direction. Once I had all my forces identified and laid out properly, it became much easier to see which forces balance, and which ones don't and then I could solve for the missing value. An example of this would be dealing with the force of friction on an inclined plane. Depending on the direction the object is moving, the force of friction could be going either way on the ramp, therefore it was extremely important for me to draw the correct free body diagram, and have the force of friction going the correct direction, which is opposite to the way the object is moving.

Vector Kinematics Application

Projectile motion is something we see everyday day in our lives, and a good example of this, is golfing. Many sports display projectile motion, such as football or basketball, but golf has always been a sport that I have enjoyed since I was a little kid, going to the driving range with my dad. Hitting a golf ball with a club creates a parabolic trajectory that is caused by the effect of gravity on the golf ball. We can calculate how far and how high a golf ball will travel, using the principles of projectile motion.

The initial velocity of the golf ball has a vertical and horizontal component. The initial vertical and horizontal components can be found if we know the angle the golf ball was hit, using the equations: Vo horizontal=Vo cos θ and Vo vertical=Vo sin θ, Vo being the speed with which the club hit the ball. The launch angle affects the vertical and horizontal components as seen in the equations above, therefore the launch angle can affect how high the ball will travel, and how far it will travel.

http://sportsnscience.utah.edu/the-in-depth-science-of-golf/

Due to gravity, there is a downward (vertical) acceleration, however, there is no horizontal acceleration, therefore, Ax=0, and Ay=-9.8m/s^2. This means that the horizontal component is moving at a constant velocity. With the horizontal acceleration being 0, the range, or the horizontal distance the ball travels, can be calculated using the equation, Dx=V horizontal × t (time of flight). However, the vertical motion is different as we have to deal with an acceleration due t =o gravity. The vertical component of the initial velocity is upwards, however we have to account for gravity, which is pulling the ball towards the ground, therefore we use the formula, Dy=Vo(y) × t + 1/2 at^2 to find the vertical distance the golf ball travels.

Air resistance, and wind can play a significant role on the trajectory of a golf ball, however this explains why golf balls have dimples to reduce these affects. Although we usually do not account for air resistance in problem solving, this diagram shows an interesting fact that I have learned through this journal entry.

http://io9.com/5606110/why-golf-balls-have-dimples

Projectile motion can be seen almost anywhere, but golf is a sport that solely relies on the trajectory of the ball and where is lands, which really shows the importance and application of projectile motion.

Vector Kinematics Reflection

To start the year off, we began learning about 2D vectors, relative velocity, and projectile motion. Coming from IB Physics SL 11, these topics were familiar to me, however, I found it beneficial to study these topics in greater detail, and spend more time on each topic.

When learning about 2D vectors, we learned methods of adding and subtracting.  We learned components method, which I had learned last year, but was difficult to remember. Components methods involved drawing each vector separately. Each vector has an x component and y component using trigonometry to find the values of each. Once we have the components, we can either add or subtract the x components of each vector and the y components of each vector and resolve them into 1 x component and 1 y component. With these vectors, we can add or subtract them, by solving the right triangle they create. The magnitude can be found using the pythagorean theorem, and the direction can be found using trigonometry (SOH CAH TOA).

Next we learned about relative velocity, and how all motion is relative to an observer. This made us look at what a velocity was relative to. For example, 2 cars are driving side-by-side at 50 km/h. A person is standing on the side of the road and watches them drive by. The person standing on the side of the road sees the cars pass at 50 km/h, however relative to each other, the people in the car would not see each other move because they are moving at the same speed. We used subscripts to represent each of the velocities relative to each other and used a vector sum to find the velocity of a moving object, relative to the ground.

Lastly, we learned about projectile motion in 1 and 2 dimensions. Projectile motion in 1 dimension was review from Physics 11, however projectile motion in 2 dimensions was a bit more difficult. At first we focussed on projectile being launched horizontally. We also watch a video on Myth Busters, about how an object shot from the height as an object is dropped hit the ground at the same time because they have the same gravitational force acting on them. When an object has horizontal velocity, there are 2 dimension to the motion of the object as there is vertical acceleration from gravity, however the horizontal velocity is constant. When solving projectile motion problems, we separate the horizontal and vertical motion, and use the formula, D = V_it + 1/2at². We can find information like time of flight, the range of an object, and how high an object was dropped from, amongst other information.

http://www.mrfizix.com/home/projectilemotion.htm

The biggest difficulty I had with this unit was thinking of 2D projectile motion as having a horizontal component, and a vertical component. I was used to only solving problems with an object falling or being thrown vertically. For me, it just took a lot of practice problems, and braingenie questions to get used to separating the horizontal and vertical motion then using the information I have to solve the question. Braingenie was actually quite helpful for this as the questions are a different style from the practice problems we get in class.