Work Done by a Variable Force (Vertical Effort) Experiment

UNIVERSITI KUALA LUMPUR MALAYSIA FRANCE INSTITUTE MECHANICAL ENGINEERING SECTION

Laboratory Experiment Sheet ENGINEERING MECHANICS 2

WORK DONE BY A VARIABLE FORCE (VERTICAL EFFORT) EXPERIMENT

OBJECTIVE

The 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. THEORY

In 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  s2 to another point s1, the distance of movement is classified as a displacement of the particle is represented by the differential d r  r .

Figure 1: work of a load, L When 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 de fined as a work dU , which is done by force F corresponding to the displacement d r. r. dU = F ds cos θ

By definition of dot product: dU = F . d r When a particle undergoes a finite displacement along its path, the work is obtained by integration. This work denoted by U 1→2, is U 1→2 =

r2

∫r1

s2

.d = ∫s1

F cos ∅ ds 

Where the variable of integration  s measure the distance traveled by the particle along the path, the work U 1→2 represented by the area under the graph obtained by plotting Fcos∅ versus s. If the  particle is moving in a straight line and a force Ft   is acted upon a constant magnitude and of constant direction, the component of the force Ft in the direction of displacement is Ft cos θ. The work done by Ft can be expressed as: U 1→2 =



Ft cos θ ∫ 

Or U 1→2 =

Ft cos θ (s2 –  s1)

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

Figure 2: work moving in a 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.

Figure 3: work done by varying effort This 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. Power Power is defined as the amount of work performed per unit of time. Hence, the power performed as amount of work d U  within the time interval dt  is  P  =

  

Provided the work d U is expressed by d U  = F . d r , then it is also possible to write  P  =

  .  = = F.      

Or  P  =

F.v

Analysis and discussion 1. Plot force versus mass moment of inertia for both load (theoritical and experimental) and analyze the data. 2.  Name some application by using this mechanism and explain it. 3. Discuss 2 possible source of errors (other than parallax error) and how it’s can effect the result

Endorsed by : Technical Unit Leader Sign & Stamp Date 19th September 2016

HOS/ PC Sign & Stamp Date 19th September 2016