Unit 2 & 3 Project

How are the principles of rotational equilibrium applied in triple beam balance?

Torque is a twisting force that causes rotational motion. When an object is in rotational equilibrium, it is not moving or rotating, thus the net sum of torque on the object equals to zero and the sum of the clockwise torques must be equal to the sum of the counter clockwise torques.

A real life application of rotational equilibrium can be found in triple beam balance.
A triple beam balance is a type of balance commonly used in schools, offices and laboratories to determine the mass of samples. A triple beam balance works by matching the torque resulting from the measured mass with an adjustable torque generated by balancing masses.

If you would like to measure the mass of an object using a triple beam balance, you first have to adjust the balance so it will point at the number zero. Then you place the object on the pan. Afterwards, you adjust the sliding weights called riders on the three beams, so the pointer will once again, point at zero. Once the Triple Beam Balance is balanced, you look at the riders and see what numbers they are on. That is the mass.

Here is a short video demonstrating how to use a triple beam balance

http://www.youtube.com/watch?feature=player_embedded&v=FfuBO3-K8AQh

A triple beam balance works on the principles of torque and rotational equilibrium.

Basically, if the two forces on each side of the balance point (pivot) are equal, the balance will be horizontal and it will be in equilibrium. The pointer on the balance indicates this condition. The object being weighed has a specific mass generating a fixed torque at its fixed position. The torque exerted by the riders on the other side of the pivot can be varied according to the position of the sliding weights on the beam.

These positions have been calibrated to correspond to specific weights, so when each side is balanced you can read the weight that is balanced against the object.

To be completely scientific, we are measuring torque when we use a balance beam. The amount of torque on each side will be equivalent when the beam is balanced.
Torque is calculated using the formula below:

where:
r is the distance from the pivot to the point where force is applied
F is the magnitude of the force,

As the riders move further away from the pivot, they exert a greater downward force on the beam and upward force on the pan. If the beam is balanced, it indicates that the sample and the riders exert the same magnitude of forces and therefore their masses equal since gravity is constant.

While a spring scale measures the weight of an object, a triple beam balance measures the true mass of an object, and not just weight that changes with changing gravitational force. This is because the force that is acting on each side of the pivot of the balance is gravitational force. Gravity will be constant wherever you are, only moment or torque will be relevant.

Bibliography

Torque, Wikipedia, http://en.wikipedia.org/wiki/Torque

Weighing scale, Wikipedia, http://en.wikipedia.org/wiki/Weighing_scale

Class notes

Emma’s Unit 2&3 Reflection

What I learned

In Unit Two Dynamics, we learned Newton’s Laws. There are three laws in total. The first law states that an object in motion will stay in motion and an object at rest will stay at rest unless an outside force is applied. The second law states that the acceleration of a body is proportional to the force and inversely proportional to the mass. This concept can also be represented mathematically as  F_net = ma. The third law states that for every action force there is an equal and opposite reaction force.  We also learned about different kind of forces for example gravitational force, frictional force and normal force. We use our understanding of forces and Newton’s Laws to questions that involves finding a missing force, the mass of an object or acceleration. For this type of questions we often use the formula F=ma.

We also learned how to solve more complex questions that involve inclines and more than one objects.

In order to solve this kind of questions, we first have to draw a labeled free body diagram with arrows. Then, resolve the objects’ gravitational force into its x and y component and use the formula F=ma.

In Unit 3, we learned that when the sum of forces acting on an object is zero, the object is in equilibrium. There are two different kind of equilibrium: translational equilibrium and rotational equilibrium.  Translational equilibrium occurs when all objects are at rest (static equilibrium) or moving with a uniform motion in a straight line (dynamics equilibrium). We use the formula ∑F=0 to solve problems involving translational equilibrium. We can solve a problem using either component method or closed vector diagram method.

   Component method  

  

Closed vector diagram method

 On the other hand, rotational equilibrium occurs when it is not moving or rotating and the net sum of torque on the object equals to zero. We use the equation ∑τ=0 and ∑τ_cw =∑τ_ccw  to solve problems on rotational equilibrium.

What I found difficult

I found the practices and tests in the Dynamics Unit to be fairly easy. However, the Equilibrium Unit is a bit harder for me. When I do questions involving torque, I sometimes get confused about the direction of torque. I found that the mass attached to a wall by a hinge type of questions to be most difficult. This is because these questions are more complex and there are often many forces to consider. Sometimes I am careless or trying to do the question too fast and I will miss one of the forces and get the answer final wrong. So I will try to be more careful when I am doing this kind of questions.

My problem solving skills

My strength in problem solving is I found it really easy to solve questions using the closed vector diagram method. I am also comfortable using the components method but I found this method involves more work and takes more time. I am comfortable about calculating angles using sine law of cosine law. My weakness is that I can get confused when I am finding the directions of forces. I will try to improve on my weakness by doing more practices.

Melissa's Unit 2&3 Reflection

Right now, I am more familiar with equilibrium by the end of December. Equilibrium does not only appear in chemistry (equation can shift back and forth) and business (price equilibrium), but also in physics!! There are different kinds of equilibrium in physics, such as, translational equilibrium, rotational equilibrium, static equilibrium. Translational equilibrium means all the objects at rest or moving with uniform motion in a straight line. The sum of the forces acting on the object also equals to zero. I think solving problems related to translational, equilibrium is my strength in this unit and I think the problems are fun and interesting to deal with. At first, I had difficulties by drawing triangles. However, I never gave up and practiced a several times at home. Now, it becomes my strength and I am happy to see myself improve on that. The second one is rotational equilibrium and it is a bit similar with translational equilibrium, which is when the net torque on an object is zero, it is said to be in rotation eq’m. Torque is the twisting effect caused by a force and it is affected by the position of the force (angle) and also the magnitude of force. Rotational motion or angular acceleration is caused by net torque. Problems related to rotational eq’m are also easy to understand. Somehow, I find they are sometimes challenging too! Thirdly, static eq’m means that an object is not translating and not rotating. However, I think some problems related to ladder, beam problems, deal with torque and angles are a bit challenging for me. For some of the beam problems, I always keep forgetting to put cosine angle something and I also lose mark on that on my test. It is important to understand what forces are extracting on the specific object while you are working on the eq’m problems. Also, practice more problems also helps a lot on my study. 

Group Project

How are the principles of projectile motion applied in badminton?

Projectile motion is a form of motion where an object is thrown at an angle not equal to 90 and it moves along a curved path due to gravity. The principles of projectile motion are applied in badminton. The motion of a shuttlecock in play can be demonstrated by the concept of projectile motion. The shuttlecock can be considered as a projectile and it follows a path called the trajectory.

The trajectory of a shuttlecock is similar to the diagram below, where the horizontal component of its velocity stays the same while the vertical velocity changes due to gravity. The vertical component of velocity undergoes a positive acceleration until the projectile reaches its maximum height where the vertical component becomes zero, and then the velocity accelerates negatively.

 

 

Factors affecting the trajectory include gravity, air resistance, speed of release, angle of release, height of release. In this case, the effect of air resistance can be neglected, since the acceleration of the shuttlecock is only caused by gravity. The gravity on earth is the same which is 9.8m/s². We will focus on air resistance, speed of release, angle of release, height of release.

 

First, the angle of release has a great impact on the trajectory of the shuttlecock. As the angle increases, the range (horizontal distance that the shuttlecock travels) increases and vice versa.  However, the speed of release has to stays the same. For example, if the angle of release is 30 degrees, the initial velocity is 15 m/s and the time is 2 seconds

The range can be calculated using the formula, Dx = Vix × t

Dx = (15m/s)cos30° × 2s = 26m

If the angle of release increases to 40 degrees whiles the other values stay the same. The range will decrease to 23m. Dx = (15m/s)cos40° × 2s = 23m

 

 



Second, the speed at which the shuttlecock is released influences its trajectory. The harder the shuttlecock is being hit, the larger initial velocity (speed of release) and therefore increasing both the vertical and horizontal distance it will travel. The less strength you put in hitting it, the smaller the distance that will result.  

Finally, the height of release also plays an important role in the trajectory of the shuttlecock. The higher the level of release, the greater the distance covered in flight. This is because the higher it is released, the longer it will stay in the air and therefore the horizontal component of the force will be acting on the shuttlecock for a longer period of time. This means that if a person jumps up and hit the shuttlecock at a very high level above the ground, the birdy will go further in distance.

In conclusion, understanding the concept of projectile motion will help us to play badminton better.

Emma’s Reflection

This is the first time I have ever taken regular physic course. Last year, I was in the IB Physics SL 11 class. I found that IB is not suitable for me since I am not considering going to study in the States. Last year, I did very well in IB physics. My final mark is an A. So I have confident that I can do well this year in regular physics class. However, having too much confidence is not really a good thing because I found that I am not spending as much time in studying and doing questions as last year. This is because I thought that I have already learned these stuff last year that I don't need to study as much. In fact, i found that I have forgotten "everything" because I have not look at physics stuff since summer break started. I need to refresh my memories. Moreover, a lot of the things I learned this year are different from what I have learned last year. This is because there are many different methods for solving a single question.

From now on, I will spend more time on studying and doing practice questions. I also have difficulties in memorizing formulas. Although the formula sheet is provided during tests, there are still a few formulas that are not on the formula sheet. I found it very difficult on memorizing formulas and I often mix up different formulas. Sometimes, I even mix up the positive/negative sign of a value and I will end up messing up the whole calculation and get an incorrect answer.

I found that doing practice questions is a very effective way to learn. It will not only help you to understand the concept and be more familiar with different kind of cases, but it will also help you to memorize the specific formulas that are used in solving that kind of questions.

Melissa’s Reflection

It has been two months since I took physics 12 in this school. I learnt a lot within these two months. I learned about vector, kinetics, projectile motion, how to calculate the magnitudes and directions. I faced some difficulties while i was studying physics. Sometimes, I don’t get the question and i have a difficult time on drawing the diagram out. Without the help of diagrams, it is impossible for me to finish the physics question. Secondly, for substituting the values into the equation, i always mix up the initial and final velocity. Thirdly, i had difficulties on calculating the horizontal velocity Vx and vertical velocity Vy.

In order to solve all my problems and have a good result on the test, I did many questions about velocity, motions kinetics, vector and magnitude... until i get used to the format of the questions. If I don’t understand a question, i usually ask my teacher for advises and ways to solve the problems. After practising for a while, my understanding of questions improved and can draw diagrams right after reading the question.  I can also calculate V_x and V_y immediately by using cosine, sine or tangent. Finally, my weakness that I have to improve is lack of understanding of a question and strength is using formulae to find the results of the questions.