Work Done By A Variable Force (Vertical Effort)Experiment

ObjectiveThe objectives of the experiments are to demonstration the work done by a variable force(vertical effort). This experiment also investigates as area under the graph of force by carries a different load and the distance when it moves.Apparatus 1. Bench-top2. A vertical board with two pulleys with ball bearings3. Rope4. Two weight hangers5. Weights set6. Load hanger7. Stainless steel Ruler8. PencilTheoryIn mechanics a force F does work on a particle only when the particle undergoes a displacement in the direction of the force. Consider a particle is move from one point to another point ,the distance of movement is classified as a displacement of the particle is represented by th differential dr.

21d121LLFigure 1 : Work of a load,LWhen a force causes displacement of a body, work is done. By work its mean mechanical work,as defined in physics. From this relationship a scalar quantity can be defined as a work dU,which is done by force F corresponding to the displacement dr.

ForceDisplacement, Figure 3 : Work Done by varying effortThis experiment is designed to reinforce the general principle that the work done, particularly by a variable force, can be determined simply by measuring the area under the graph of force and distance moved. The apparatus is a simple lifting mechanism with obvious non linear characteristics. A suspension cord carrying a loaded trolley at mid span is tensioned by passing the cord over a pulley at one end and down to a weight hanger. As the vertical effort is increased, the tensioned cord will move to a new equilibrium position lifting the loaded trolley.PowerPower is defined as the amount of work performed per unit of time. Hence, the power performed as amount of dU within the time interval dt is

Provided the work dU is expressed by dU = F.dr, then it is also possible to write

Or By definition of dot product:

When a particle undergoes a finite displacement along its path, the work is obtained by integration. This work denoted by , is

Where the variable of integration s measure the distance traveled by the partical along the path, the work represented by the area under the graph obtained by plotting versus s. If the particle is moving in a straight line and a force F, is acted upon a constant magnitude and of constant direction, the component of the force F, in the direction of displacement is . The work done by F, can be expressed as :

Or Work done can be represented graphically if we plot force versus displacement. The area under the curve represents the work done.

ForceDisplacement,Work,LFigure 2 : Work moving in straight line (vertical effort)By doing this experiment we will using a different load and rearrange a distance to be stay in equilibrium position. Form different load and distance, work done will obtain. This is an example, the work done by a varying force in moving an object between two points is equal to the area under the curve between these two points.

Procedure1. Put the 500g weight on the load hanger.2. The vertical distance from the base of both load hanger and vertical effort recorded.3. Apply 300g weight on the vertical effort load hanger.4. When the system is in equilibrium repeat step 2.5. Repeat steps 3 and 4 with another load 350g,400g and 450g.6. Apply 2 of 500g weight on the load hanger.7. Repeat process no 2 to no 5.8. Repeat the the same process 3 times to get accurate results.

Data Result

Experiment 1stLoad = 0.5kg = Gravity = 9.81Load (g)Force (N)Displacement(m)

0000

500.4910.0910.045

1000.9810.1430.140

1501.4720.1710.252

2001.9620.1820.357

Experiment 2ndLoad = 0.6kg = Gravity = 9.81Load (g)Force (N)Displacement(m)

0000

500.4910.0920.045

1000.9810.1390.136

1501.4720.1650.243

2001.9620.1850.363

Graph

DisscussionThis experiment there are some things that need to be discussed among which are the source of the error and use in industry. Among the sources of error in this experiment there are friction at the pulleys, that error can be ignored because of no calculation are related about friction. In addition, size of both pulleys also can be ignored because no specific details about the size and types of pulleys that has been used. Vibration also are types of error can be discussed because, vibration exist during the experiment running, its came from factor of surrounding. Futhermore, reading error also can be classified as source of error, when the results came out, the people who took the result should be alert and aware about how to do calculation and the data they need to complete the graph. The error on the hanger load can also be ignored because the purpose of the experiment to analyze the difference distance from the initial point to the end point , this experiment also to studying how much mass needed to attract mass remains found on the hanger load. For application this concept are mostly used in the industry such as logistics sector , construction sector and large industries that involve heavy work .

ConclusionThe conclusion of this experiment is to find out how much difference the work done by the method of theory and practical. In addition, its also to knows how many error exist that prevents us from obtaining accurate results or those anticipated. But also, this experiment can also help and teach us about how to reduce and fix the errors found in this experiment, and it can also help us to repair existing equipment in industry.