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.