Mouse Trap Car Design

Unit 5 Blog Post

Unit 5 Blog Post

            This unit we learned about work, power, kinetic energy, potential energy, the conservation of energy, and machines. I thought this unit was particularly cool because throughout the chapter we could see how all the physics concepts related to one another.

            Work is the effort exerted on something that will change its energy. Work equals force times distance. [Work=Force X Distance] Work is measured in Joules. The force and distance must be parallel to one another in order for there to be work done.

            For example, this is a waiter carrying a tray. I automatically assumed that work was being done on the tray. However, there is NO work being done on the tray itself. The force, which is the tray, being pulled down by gravity is not parallel to the horizontal distance the tray is moving.

However, there is work being done on the tray when the waiter lifts the tray. The force of the tray moving upward is parallel to the vertical distance the tray is lifted.

            Here is another example of work. You have the option to take the steeper hill or the more gradual side to get to the field hockey field, yet both sides will take you the same vertical distance. Therefore, the steeper side of the hill and the gradual side would require you to do the same amount of work because work is dependent upon force and the VERTICAL distance you traveled and both hills have the same vertical distance.

            The next concept learned in this unit is power. Power depends on work. Power is equal to the amount of work done per time it takes to do it. Power is measured in watts. The faster work is done, the more power there is.

[Power=Work/Time Interval] Power is measured in Watts. The amount of power is dependent upon how quickly work is done. The faster work is done the more power there will be. But remember the amount work done does not factor any time unit; it is power that depends on work and time.

            In class we had a lab involving walking/running up and down the stairs. The amount of work done when we walked up the stairs versus when we ran up the stairs was the exact same amount because the force and distance did not change. However, the power of walking versus the power of running up the stairs changed because the amount of time it took to go up and down the stairs changed. There was more power when we ran up the stairs because it took less time to complete the work. The faster the work, the more power there is.

            The next concepts we learned about were kinetic and potential energy.  Energy is the ability to do WORK. These two energies come from mechanical energy, which is the energy due to the position of something or the movement of something. Mechanical energy can be in the form of potential, kinetic, or a sum of the two energies. Potential energy is energy that is stored and held in a stored state that has POTENTIAL of doing work. Potential energy is equal to the combination (multiplied) of mass, gravity, and height.

[Potential Energy= Mass X Gravity X Height] A simple example of potential energy is a ball sitting on the top of a cliff about to fall. Another example involves a bow an arrow. When a bow is drawn, energy is stored in the bow. 

            Kinetic energy is the energy of motion. Potential energy can change into kinetic energy. The change in kinetic energy of a moving object depends on the mass of the object as well as its speed.

[Change in Kinetic Energy=1/2mass X velocity^2] Anything in motion has kinetic energy. According to the work energy theorem, work equals change in kinetic energy. Potential energy and kinetic energy are both measured in watts because they are both forms of energy and energy depends on work. Whenever work is done, energy is exchanged. 

            The next concept we learned was the conservation of energy. The conservation of energy states that energy cannot be created or destroyed; it may be transformed from one form into another; but the total amount of energy never changes. When you think of a system, like a swinging pendulum, there is one thing that is neither created nor destroyed, and that would be energy. The energy may change form, for example, it may turn into heat, however, that does not mean the energy is lost. Take a water dam for instance. The water behind a dam has energy that may be used to power a generating plant below, where it will be transformed to electric energy. The energy will then travel through wires to homes where it can be used for everyday uses. Because we know energy does not disappear or appear, it transforms, we can assume that kinetic and potential energy can transform into one another. Here is an example that can help to explain this concept.; Imagine a ball at the top of a cliff about to fall off,  at the top JUST before the ball is falling, it has 10,000J of PE and it has 0 KE. However, as the ball falls, its potential energy decreases and its kinetic energy decreases. However, the total amount of energy remains at a constant 10,000J. Right before the ball hits the ground, its potential energy has decreased to 0J and its kinetic energy has increased to 10,000J. Here we see the transformation of energy.

            When you think of a machine, you might assume it’s a complicated device. However, machines can be very simple. A machine is a device for multiplying force or simply changing the direction of force. Machines reduce or change force but NOT energy and work. The principle of machines comes from the conservation of energy. When you put work in there is an equal amount of work out.

[Work in=Work out] Since work equals force X distance…

[Force in X distance in = force out X distance out] Suppose you are loading a box to a truck. It will take much more force to load the box with a shorter distance than it would be if you were to add a ramp.

Work in (the ramp)= fd

Work out (without the ramp)= fd

Work in=Work out

fd=fd

An ideal machine would work with 100% efficiency. However, all machines have some sort of transformation of thermal energy. If we put in 100 J of work and get out 98 J of work, that machine is 98% efficient. It did not LOSE energy, it just wasted 2% of its energy because that 2% was transformed into heat.

As I mentioned before, this unit ties a lot of its concepts together. This is an example to show this connection of terms:

A 10kg car accelerated from 10m/s to 20m/s in 2 seconds. In that time it traveled 10m.

The change in Kinetic energy the car experience?

Change in KE= 1/2mv^2

Change in KE before= Change in KE after

Change in KE final- Change in KE initial = Change in KE

1/2mv^2 final - 1/2mv^2 initial= Change in KE

½ 10(20)^2- ½ 10(10)^2= Change in KE

½ 10(400)- ½ 10(100)^2= Change in KE

½ 4000 - ½  1000= Change in KE

2000-500= Change in KE

1500J= Change in KE

How much work was done?

Work= Change in KE

Work= 1500J

What was the force that caused the car to accelerate?

Work= fd

1500=F(10)

Force=150N

What was the power during the acceleration?

Power=Work/Time

Power=1500/2

Power=750 Watts

This unit I started out strong with the concepts of work and power, however, I struggled a lot with potential and kinetic energy. I was confused with how they could transform into one another. I especially struggled with the questions asking about the potential, kinetic, and total energy throughout the fall of an object. However, after struggling on an open note quiz, I realized that I needed to clarify whatever was confusing me. So, I looked at the Eureka videos, which helped to clarify my confusions.

            My problem solving skills this unit stayed fairly steady. Once I had clarified my confusions with kinetic and potential energy it was easier for me to make connections between all the concepts. The six problems we did in class were a really useful tool for bringing these concepts together. After going over these problems, my problem solving skills were strong and clear. Although I had a high effort in homework and I always take diligent notes, I did poorly on an open note quiz. This was because although I had the notes and homework, I didn’t have as clear of an understanding as I should have. So, next unit my goal is to catch my confusions like this early on so that I don’t face another poor open note quiz. 

Our podcast had some technical difficulties but our group worked well together, we all collaborated our ideas and my ideas about work were clarified and corrected like on the waiter example. Instead of saying there was no work being done (when the waiter was carrying the tray) I was corrected to say that there was no work being done on the TRAY. 

Unit 5 Photo

Here, it may just look like a foot, however, it is really displaying multiple concepts of physics! If these feet are walking, and someone asks “How much work are they doing?” The answer is that whoever is walking is doing NO work. Work is equal to force times distance.  In order for there to be work, the force and the distance must be parallel to one another. In this instance, the force is the person (vertical) and the distance is horizontal therefore the two are no parallel to one another, meaning there is no work being done. Because there is no work being done, there is no power since power is equal to work divided by time. Power is measured in Watts. However if the person walking began to walk up a flight of stairs, then there would be work done. This is because the force and the distance would be parallel. The vertical distance and the vertical force would determine your amount of work, which is measured in Joules.  The time in which you completed the work being done would determine your power. 

Unit 4 Photo

Torque causes rotation. It is equal to force multiplied by lever arm [torque=force X lever arm]. The farther the lever arm is from the axis of rotation, the less force is required for an object to rotate. A paddle is required in order to kayak. One of the key points of this paddle, is how you hold it. The farther apart you place your arms, the easier it will be to paddle because the lever arm will be increased and the force required to move the paddle will be much less than if you were to hold the paddle with your arms close together. Although your rotational inertia would decrease because you would be holding the paddle closer towards its axis of rotation, the lever arm would be decreased therefore the force required to move the kayak would increase.

Unit 4 Blog Reflection

            This unit was particularly interesting because the physics we learned seemed to relate to ever day activities even more than before.  There are three main topics we learned about this unit; rotational and tangential velocity, rotational inertia, the conservation of angular momentum, torque, center of mass/gravity, and centripetal and centrifugal forces.

            Rotational velocity is the number of complete rotations per time unit. Tangential velocity can also be called linear speed because it is something moving a long a circular path. The direction of motion is tangent to the circumference. Tangential speed depends on the distance from the axis of rotation. Take a merry-go round for instance, the closer you are to the middle the slower you are going whereas on the outside you feel as though you are going much faster. This is because the people on the outside are farther from the axis of rotation. Everyone has the same rotational speed. Their rotational speed is dependant upon the number of spins the platform of the merry-go round has per time unit.

Another example is a track race. If everyone started in an exact straight line, the race would be unfair because the people on the outside would have to have a greater speed to keep up with the people closer to the axis of rotation who would not need to go as fast. The runners on the outside would have a greater tangential velocity than the runners on the inside. Each runner has his or her own rotational speed depending on the speed in which they are going.

Have you ever seen a car with tires much too big for its frame? Well these people most likely get speeding tickets frequently if they are not careful. A speedometer is accustomed to a specific size of tires, therefore when you get larger tires than the speedometer is accustomed to the car might read 40mph but you are really going 60mph. Although your rotational speed decreases, your tangential speed increases and you are covering a greater distance in a smaller amount of time because your wheels are larger.

The last example we learned a lot about is the wheels of a train. The wheels are designed with the wider parts in the middle rather than the outside. The wider parts are in the middle because the wider parts will allow the wheels to turn and go straight. The smaller parts of the wheel will want to turn and the larger parts will direct the wheels to remain on the tracks. In this scenario the left diameter on the track is smaller than the right therefore it will move slower and the right will move faster causing the wheel to curve inward. If it shifts too far where the larger diameter is on the left, it will move faster causing the train to curve in the opposite way, it is a method of self-correction.

Moving on to rotational inertia; Inertia is the property of an object to resist change in motion dependant upon the mass. Rotational inertia is the property of an object to resist changes in the spin of an object. It is dependant upon, not the mass of each object, but where the mass is located on that object, how it is distributed.  It involves the distribution of mass and how far away it is from the axis of rotation. If an object has a small amount of rotational inertia, it is easier to spin compared to an object with a large amount of rotational inertia, which is very difficult to spin.

Rotational inertia explains why runners bend their legs instead of keeping them straight. By bending their legs, their mass is closer to the axis of rotation lowering the rotational inertia.

This can also explain how an ice skater spins. When the ice skater has their leg and arms spread out and spinning, their rotational inertia is much greater because her limbs are farther away from his/her axis of rotation, therefore the ice skater is spinning very slowly. However, if an ice skater brings in his/her arms and legs, her rotational inertia decreases because she is bringing her mass closer to her axis of rotation.

The conservation of angular and rotational momentum is basically the same concept as the conservation of momentum. Angular momentum is made up of two key factors: rotational inertia and rotational velocity.  Angular momentum before equals the angular momentum just as the total momentum before equals the total momentum after.

Conservation of Angular Momentum:

Rotational inertia X Rotational Velocity (before) = Rotational inertia X Rotational Velocity (after) 

Here’s an example of the ice skater with angular momentum;

RI X rv (before) = ri X RV (after)

In this example, the ice skater started out with a large rotational inertia (because she had her mass far from her axis of rotation) therefore she had a small rotational velocity. Then, she had a small rotational inertia (because she brought in her mass closer to her axis of rotation) and had a large rotational velocity. We know this is true because of the conservation of angular momentum, which informs us that the momentum before will always end up equaling the momentum after.

            Torque is what causes an object to rotate. It equals the force of an object multiplied by its lever arm (which is the distance from an object of rotation). If an object has a large torque, it will have a large torque.  A torque is the rotational counterpart of force. Force changes the motion of objects whereas torque changes the rotation. Just like rotational inertia, torque involves the distance from the axis of rotation. This distance with torque is known as the lever arm.

            In this example, the ball on the left is hollow, therefore it a smaller force than the ball on the right who has a larger force and although the both the ball on the left side of the seesaw and the ball on the right side of the seesaw have equal lever arms, the ball on the right has a greater torque because it has a larger force therefore it has a larger torque.

            However, in this image notice that the lever arm on the left is larger than the lever on the right. Therefore, the small force and large lever arm on the left balance out the large force and small lever arm on the right. The lever arm on the left was increased by simply having a greater distance from the axis of rotation.

            This is also common when dealing with bolts and wrenches. If there is a tight bolt, you would want to have a wrench with a large lever arm because by just creating a greater distance from the axis of rotation the force required to turn the object will decrease and the amount of torque will be greater. 

            The center of gravity is a term commonly used to express the center of mass. The center of gravity is the average position of weight distribution. Center of mass and center of gravity refer to the same point of an object. The center of gravity must be above the base of support. When the center of gravity is outside the base of support a torque happens. The center of gravity lies directly beneath the point of suspension. The center of mass of an object may be a point where no mass exist.

            An example where we see the center of gravity is the Leaning Tower of Pisa which has the center of gravity lying above its base of the support therefore the tower does no fall over. An object with a wide base and a lower center of gravity is more stable.

            A centripetal force is a center seeking force. A centrifugal force is a center fleeing force, however, it is a fictitious force. Think about a car going around a turn. The friction between the tires and the road provides the centripetal force that holds the car in a curved path. However if the friction is not great enough, the car will skid off the road.

            However, inside this rotational system there seems to be an outward force. This outward force is the centrifugal force. An example that might be able to explain this more easily would be if you were a passenger of the car that was rounding the turn. The car is turning left and you move outward to the right, technically this was not because of a centrifugal force, it was because there wasn’t a centripetal force to keep you in a circular motion.

            This unit was surprisingly difficult for me. The concept I struggled with the most was torque. I was confused by the difference between torque and rotational inertia. However, after going into conference period, I realized I needed to re watch the torque video. In doing this, I mastered the concept and I examples in the book involving torque.

            My problem skills throughout this unit progressively increased. At first, I struggled with going into depth with each of the concepts presented to us. I didn’t realize that I wasn’t going into enough depth until I began struggling with torque. I realized I needed to be able to relate each of these concepts to one another. So, I reviewed my notes from the previous videos and tried to find any gaps I didn’t understand. To clarify my confusion on specific example, I discovered that the book is actually really helpful. I think that was my key discovery in my problem solving skills this unit (the book). My homework effort this unit was very high and I didn’t miss an assignment and each assignment I completed I didn’t think was just busy work, it was helpful when looking back and studying it. Although I had a high effort in homework this unit, I need to work on my participation in class. I am always focused in class, yet I don’t raise my hand enough to ask questions or to answer questions. I think this could really help me with clarifying concepts for me.

            Our podcast was a little frustrating because our group had a hard time coming up with what to say, however, the product ended up as a really great study tool. 

 http://www.youtube.com/watch?v=YEI_3ES1PR8&feature=youtu.be

Mass of a Meter Stick

My original plan for solving this challenge problem worked, however, it was much more complicated than it needed to be. We decided we would just come up with a plan along the way. Naeem and I constructed a seesaw instead of a countertop like the rest of the class. We rested the meter stick on a book with the weight on one end and balanced the stick so that it appeared horizontal. When doing this it was apparent that the side with the weight on it had a larger lever arm than the side with the other weight. This is when we took the formulas about torque and put them to use. The original formulas used:

 t=t

t=force X leverarm

force X leverarm= force X leverarm

w=mg

clockwise torque= counter clockwise torque

After taking measurements we knew that the meter stick was 100cm. The side with the weight had a lever arm of 28cm and the side with the meter stick balanced on it had a lever arm of 22cm. We also knew that the side with weight had a force of 98. This is because the force on it was the force of gravity and converting that to Newton’s it would be 98.

            28 X 98= 22 X F

            2744=22F

            F=124.727N

The force of this really wasn’t far off yet this process became a lot more complicated than it needed to be when the see-saw was made. So, we followed the common method used by the class even though we got similar answers either way. In the correct process we balanced the stick and the mass off a tabletop. It took out the variable of the extra meter stick and we also got different numbers. However the lever arms ended up in the same proportion (the side with the weight had a larger lever arm than the other side). Another thing that changed in this were the decimal points. We realized that last time we had moved the decimal points of the force of gravity had been moved to the right instead of the right so it actually should have been .98 rather than 98.

            20 X .98= 30 X F

            19.6=30F

            F=.653N

            .653=9.8m(w=mg)

            m=.06663g

            Answer:66.6g

Torque Source

http://www.youtube.com/watch?v=8bvXknbjIog

You don't need to watch the whole video if you have a full understanding of the basics behind torque. This source really helped me with a better understand behind torque. I liked the examples used to explain it. Although we went over the wrench example in class, it helped to have other examples with similar explanations too.
After completing homework assignments, lessons from class, and watching this video, this is my understanding of torque; Similar to a force, which is a push or pull, torque is almost as simple, it is a twist to an object. Speaking mathematically, torque is forceX the lever arm. Torque is mainly effected by these two factors (the force and the lever arm).