Andy's reflection on torques, pulleys, equilibrium, and inclines

After being taught torques, pulleys, equilibrium, and inclines in class, I now see a better understanding of how things work around me that puts these physics into work.

Things I Learned

There were many things that I learned through the months. For one thing, when dealing with an object on a ramp, gravity is not affecting the object horizontally, but also vertically, which means that I will have to break it down into x and y components. These problems can be tricky when dealing with them at first, but once you get the hang of it, it can be easier.

Gravity broken down into x and y

For equilibrium, there are two conditions an object must have to be in equilibrium. First, to be in translational equilibrium (it can be at rest or moving with constant velocity) the sum of all forces exerted is zero. Second, for an object to be in static equilibrium, the sum of all the torques from the forces that exert on the object is zero.

Pulleys are the last thing i learned. I always thought that if one side of the pulley is heavier, the tension is different. However, once this topic was taught I learned that the tension in the rope is the same as the other side and also the acceleration of the masses are the same. When trying to calculate the tension of the rope I will need to break down the system to calculate it.

Things I Found Difficult

There were many things that I found difficult. Problems that gave more info messes me up because it can be tricky, which will make me use the wrong formula or plug in wrong numbers. Also, when the rope is slanted when doing pulleys, it confuses me because I don't know whether or not to use different angles or use sine, cosine, or tangent.

Problem Solving Skills

I noticed that doing practice problems instead of reading notes helps me more because I am actually doing problems and showing work which shows how the problem is being solved. Also, If I don't draw free-body diagrams, it can be harder for me to solve the problem because the free-body diagram helps a lot because if I'm doing a pulley system, for example, drawing one will show which way the acceleration will be moving in.

Jeffery Shen's reflection on application of Newton's laws and equilibrium

We have been studying static equilibrium, pulley system, inclines and  torque for the past 2 months. In these two months, I practiced and learned how to apply the newton's laws and the principle of torque efficiently. By studying newton's laws and torque, I have now gained a better understanding of how physics can be applied into real life problems. In the following paragraphs, I am going to briefly introduce you to the wonderful world of newtons laws, how can it be applied and torque.

Newton's three laws are:

• Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it 
• F=ma, when an unbalanced force acts on an object it accelerates the object in the same direction ( of force)
• For every action there is an equal and opposite reaction( force occur in pairs). 

Although the laws seems very confusing at times, it is easy to understand if we think of the phenomenon that occurs around us.
For example, when we skate freely on a completely smooth ice, we will be traveling fast and far. However, if we wear our normal shoes and try to skate on a dry concrete floor, it is very unlikely for us to glide. This is because when on smooth ice, there isn't much of an external force to act against us, but on concrete floor, we would experience such force AKA friction.

The second law is the most powerful among the three, because it can actually enable us to perform calculations of dynamics. The formula F=ma is considered as the gold physics formula of high school.

The third law is also very easy to explain, imaging when you kick the wall really hard, the chance of you breaking your toes is pretty high. Force occurs in pairs.

Through understanding the newton's three laws, we can apply them to questions and real life problems.
In pulleys, when we consider the question as a whole system, it is mg+Mg=(m+M)a. Because neglect friction in pulleys, the only force acting is gravity.
If we need to calculate the tension in the rope, we need to split the system apart. However, the acceleration of the two masses and the tension in the ropes are the same.

The newton's laws can also applied to ramps. In ramps, because there is an incline, the object is not horizontal to the floor, so we must split the force of gravity into x and y components. Again, if we can identify forces acting on the object, it is easy to manipulate the laws and get the correct answer.

When a system is in static equilibrium, or translational equilibrium, it MUST have zero acceleration. Zero acceleration doesn't mean it has zero forces acting on it, it means the forces acting on the object are cancelled out. A good example is when we hang a picture on the wall, the rope or nail on the wall must provide enough amount of force to keep the picture from falling. The force exerts by the nail or tension in the rope cancelled out with the force of the gravity.

A nail or a rope must provide enough force to keep the picture from falling

When a system is in rotational equilibrium, all forces pass through a common point. Such force is called concurrent forces. torque=Force*distance of the from the pivot point. A good example of rotational equilibrium is a balanced balance. A balanced balance will not rotate or dip to either side. Because the two objects has the same force acting downwards, and the distance from the pivot is the same.

A balanced balance

What I found difficult about what I have studied is actually the identification of forces. Sometimes, when the questions get complex, cannot solve in simple steps and requires multiple steps, I become confused, or even anxious. It is easy to misidentify the forces and how they affect the system.
However, the above mistake can be solved by doing problems and analyzing different types of questions.

The hard part of torque is when the beam becomes slanted, it is easy to misidentify and calculate the distance from the pivot point to the rope. Especially when the rope is not perpendicular to the beam.
I solved the above hardship also by doing more problems and analyzing different types of questions. I found out that physics is learned the best by actually doing work, reading notes over and over again would not improve problem solving skills.

My problem solving skills got better through the two months of studying. I learned to analyze and find out useful information out of the diagram. I became more confident about my problem solving skills, also by doing different types of questions I felt I'm now more insightful.

I'm now comfortable with questions that involve multiple steps or require great logic. Since physics is not only about doing problems, I have also applied the knowledge I have learned to rigging tackles and explaining mechanical advantages of pulleys in sea cadets.

Overall, I really appreciate the boost in knowledge and problem solving skills that dynamics and equilibrium had brought to me. I am now more confident to learn harder and more logical concepts of Physics.

How the design of bridges relates to torque

Physics is the fundamental tool used in our lives. However, as you may not notice, the architecture of buildings, the design of the shape of our cars, and many other fields related to engineering are all applied physics. In this case, our topic is how the design of bridges relates to torque.

As you can see from the picture, there are two pillars that support the bridge from falling into the river. The two supports are very crucial as they must provide the same normal force in order to keep the net torque zero. That means the bridge should be firm and secure, not rotate around.

However, things are not so simple as just to keep the bridge secure and not rotate. Bridges are designed to be used by cars and passengers that want to cross the river safely. Therefore, engineers are faced with another challenge which is to know how much force will act on the supports when cars are passing by. We obtained a simple scenario where only one car is crossing the bridge. 

Suppose that the car weighs 1ton (1000 kg), and the bridge weighs 100tons (100000kg) how much force will each of the support exert in order to keep the net torque= 0?

we set point A to be the pivot point
Let's calculate Fb first:

(1000kg*9.8m/s/s*6.0m) + ( 100000kg*9.8m/s/s*10.0m)= Fb*20.0m

Fb= 492940N

Now we can calculate Fa:

Fup=Fdown

492940N+Fa=9800N+980000N

Fa= 496860N

It turns out that each of the support is enduring so much force. Although it seems quite easy to calculate and see the results for this simple scenario, in real world engineers have to consider other factors that will affect the stability of the bridge such as: wind, current of the river, rain or snow that will accumulate on the surface of the bridge, and many other potential situations. Therefore, it is important for engineers to think of good  framework that can better support the bridge.

Through hard work and research, the engineers finally came up with many different types of bridges. For example, a suspension bridge. Suspension bridges use thousands of steel cables to "pull up" the bridge from falling. With the cooperation of the cables and the supports of the bridge, the load capacity of the bridge increases.  A famous and well known suspension bridge is the Golden Gate Suspension Bridge located in San Francisco, California, USA.

USA's Golden Gate Suspension Bridge

Another way to increase the carrying capacity of the bridge is to have multiple bridge piers. Adding more bridge piers means that there are more supports, so the weight of cars and the bridge itself are split and  shared onto each bridge pier, each support doesn't have to exert as much force to support the bridge as compared to only two bridge piers.

China's Qiantang River Bridge

Engineers use the principles of torque to design bridges, it takes countless experiments to eventually come up with a good design. We must study hard to carry on the knowledge of physics and continue to innovate.

Andy's reflection on projectile motion

     The things I learned in class during projectile motion is that objects that are thrown will get affected by factors of gravity, air resistance, and weight. I didn't know that gravity doesn't affect the horizontal distance.  Also the weight of the object can also change the distance and the way it travels. I have also learned how to use the equations to find the projectile motion. I have also learned that many factors affect the way objects moves, like angle and the initial velocity.

     The things I found difficult in this unit is how to apply the given factors into the equations. When doing the problems, sometimes I use the wrong numbers in the equations and get them wrong, which confuses me or when i use the wrong formulas to the problem. Even silly mistakes can make my answers wrong because the question may seem easy. Which in conclusion, I should double check my answers to make sure I have done my questions right.

     My problem-solving skills depends on the work I show in the questions and the way I work in class. If i show the steps to the questions, I can have a better understanding of what to do next and will reduce the mistakes I make. My weakness is that I apply the wrong information into the equation and get it wrong.

Rafid Syed's Reflection

This is what i learned about projectile motion in soccer, any soccer ball that is being kicked is considered to have a horizontal and vertical velocity component as shown in this diagram (blue=horizontal velocity component, red=vertical velocity component).

Throughout the path of the projectile, change occurs only in the vertical direction due to the influence of gravity, while the horizontal component of the velocity will not change. (This is not quite true, there will be a very small slowdown in the horizontal direction due to air resistance).

The vertical velocity of the projectile gets smaller on the upward path until it reaches the top of the parabola. At the top of the parabola, the vertical component of the velocity is zero. After that point, the vertical component changes direction and the magnitude increases in the downward direction and the vertical distance traveled during each subsequent time interval increases.

What Ive found difficult about this topic was basically how projectile motion effected how high the object reached after being launched.

Jeffery Shen's reflection about the projectile motion

  Through learning projectile,and relative velocity I found out that I can solve more real life problems. This is the glamour of physics has brought to me.

  I learned about all the formulas such as the : d=Vi*t+1/2at^2，Vf^2=Vi^2+2ad

  Those formulas helped me to answer questions but most importantly, they helped me developing my logic, and my rational thinking. projectile motion is associated with various kinds of sports.

  An interesting thing is that the famous angry birds game is based on projectile motion. Birds being launched from a slingshot and crash on the pigs. It is so unbelievable and wonderful that people can use physics knowledge to create so much fun games!

  Relative velocity is associated with many kinds of transportation. When air-planes experience wind, the captain must adjust his plane so his plane is still on course. For navigation, the captain of the ship or boat must aim for the right angle in order to get to the point on the shore when there is a current. 

  What I found difficult about was the addition of vectors. If i added the vectors wrong then my whole question is wrong. So my study and review is mainly on get vector addition correctly.
On the other hand, the problems we are doing now are all air friction less.  If there is air friction, the height and range of the projectile travels will be  shorter and lesser. Projectile motion is relatively simple, so i don't have other problems.

  my problem solving skills improved dramatically. my logic is developed. For example, I became more comfortable with performing calculations and write out multiple steps. I learned how to use multiple formulas and steps to get my final answer. I became more proficient at drawing diagrams.In conclusion, every aspect of my problem solving skills just got better.

  Through studying projectile motion, I learned to break the horizontal and vertical motion up into two vector components.Not as in physics 11, I just simply plug in numbers into formulas and hoping to get the result. We call the horizontal component the Vx, the vertical component the Vy. Since all the problems we are doing right now are air friction-less, the Vx component does not have any acceleration. The velocity is constant for the horizontal motion. So we can ignore the 1/2*(-9.8m/s^2)t^2 part, and the formula is Vx=Vi*t. for the vertical part, if the projectile is thrown horizontally, then we can ignore the Vi part because its initial velocity is 0. if it is thrown at an angle then we just need to use cosine and find the Vyi.

  Overall, through studying the projectile motion unit, I learned that now I should not just do the problem in a simple step, I shall consider to break problems apart and solve them separately. It applies to life too, when encountering problems, i shall not expect to them right away. I shall consider the problem, plan the methods. If the problem is complex I shall consider solving them by a step by step manner, not expecting to get the answer right away.

This is a creative projectile motion video

How are the principles of projectile motion applied in soccer? (team)

       Projectile motion appears in many sports including basketball, baseball,volleyball, etc. In this blog, the sport we'll be talking about is soccer. The factors that affects the ball in soccer is gravity, air resistance, and the weight which all play a fundamental role in the principles of projectile motion.

Vx=Vi*t or 

Vx=V*sine*thrown angle if thrown at an angle

Vy=1/2*(9.8m/s^2)*t^2 if thrown horizontally or

Vy=V*cos*thrown angle if thrown at an angle

• V_y is the vertical component of the football's initial velocity
• g is acceleration due to Earth's gravity, 9.8 m/s^2 downwards 
• t is the time for the projectile from launching to landing

V_x is the horizontal component of the football's initial velocity

      In the concept of soccer, the amount of force a soccer player applies to the ball; For example, how hard the individual kicks will determine the initial velocity of how fast the ball will travel. This velocity is dictated by the initial acceleration. The acceleration is controlled by how hard the person kicks. Thus, it also determines the angle as well.

      The angle of how the soccer player kicks the ball also determines the height and distance it travelled  For example, if the ball is kicked at an angle of 45 degrees it will get the maximum range. It also affects the vertical and horizontal velocity.

      For gravity, there is always a force of 9.8m/s^2 that acts downward; thus, affecting the vertical distance of how far and high the balls travels. The gravity affecting the horizontal distance is a common misconception. This is because,  the force of gravity is always directly perpendicular and the horizontal distance is always dependent on the initial velocity. Essentially, the gravity influences the vertical distance. The gravity affects the ball because it slows down the ball as it goes up until it reaches its peak. Once this has been achieved, the acceleration will gradually speed up to reach -9.8m/s^2 until it hits the ground

      Furthermore, the air resistance also limits how high and far the ball travels as the resistance acts as a minor force which can be at times negligible. The weight of the ball can also affect how far and high the ball can travel as it becomes heavier when flying in the air.

   In terms of dribbling the ball, the amount of force applied to it will also determine how far the ball can row. Note: soccer fields are not perfectly smooth so this plays a factor. However, this is not on topic.

  The rotation of the soccer ball wouldn't  have much of an effect because the ball is spherical unlike football. In terms of football, the shape of the ball in relation to the soccer ball is very different. For football, the rotation is dictated by the shape. Because it is an oval-like object, this diversity in shape changes how the ball moves and the distance it has covered. Also, the ball may tend to spiral due to the football's shape. This is known as air drag. This affects soccer as well because both objects fly through air; forming air resistance.

  The size of the object also plays an important role in determining the air drag. The bigger the projectile, the bigger the air drag. The smaller the projectile, the smaller the air drag. The shape of the object will also affect the air drag. That is why soccer ball is sphere instead of a cube.Sphere has better aerodynamics than cubes do.

  Overall, projectile motion is very closely associated with soccer. Projectile motion is associated with almost all types of sports. Physics is very useful in our lives. Through learning physics, we can now explain some phenomena happening in soccer which we could not explain before. Thank you projectile motion unit! Let we gained good solid knowledge.