TO INVESTIGATE THE WORK ENERGY THEOREM
TO INVESTIGATE THE WORK ENERGY THEOREM
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Table of Contents
TOC o “1-3” h z u Objectives PAGEREF _Toc24617942 h 3Apparatus PAGEREF _Toc24617943 h 3Theory PAGEREF _Toc24617944 h 3Set up PAGEREF _Toc24617945 h 4Procedure PAGEREF _Toc24617946 h 5Data and Observation PAGEREF _Toc24617947 h 6Calculations PAGEREF _Toc24617948 h 7Results PAGEREF _Toc24617949 h 8Conclusion PAGEREF _Toc24617950 h 10References PAGEREF _Toc24617951 h 11
TO INVESTIGATE THE WORK ENERGY THEOREM
ObjectivesTo investigate the work energy theorem
To investigate Hooke’s law
ApparatusQuantity Equipment Part- Number
1 Motion sensor PS 2103A
1 Hi res force sensor PS-2189
1 Dynamic system ME-6955
1 Elastic bumper ME-8998
1 Elastic cord (in ME 8998)
1 Force bracket CL-6545
1 Braided string SE-8050
1 Balance scale SE-8723
TheoryThe resulting change in the kinetic energy of a body is equal to the work done to the body. This is known as the Work-energy theorem and it can be expressed as;
∆KE=work, this can be derived as W=12mvf2-12mvi2The work done by the sum of all forces acting on a particle equals to the change of the kinetic energy of the particle. It can be extended to the work done on rigid bodies.
The work energy theorem can be derived from Newton’s second law. Work transfers energy from one place to another or from one form to another. In general systems, work can change the potential energy of a mechanical object, electrical energy of an electrical device or heat energy of a thermal object.
Set upThe elastic bumper and the adjustable feet were installed on the track as shown in the figure below.
The force sensor was attached to the track by use of the bracket. The force sensor was attached to the interface and the zero button was pressed to tare the object. The motion sensor was attached and plugged to the interface. The range switch was placed on the cart icon.
Both masses were placed on the cart and the balance was used to measure their masses.
The level of the track was adjusted using adjustable feet. The cart was placed on the track and a small push was given to it away from the motion sensor. The record button was clicked to record the motion.
The level of the track was adjusted using the screw feet so that the cart moved at a constant speed as it moved from the motion sensor. The track was levelled slihtly downhill so as to eleiminate the effects of frictional forces. A short loop of string was tied to the lower tab in the PAScar as shown. A 35 cm long piece of elastic cord was cut between the sensor hook and the loop of string.
ProcedureThe cart was pulled back until stretching the elastic cord until the cart was 20 cm from the sensor. The motion sensor is placed to measure the force on the end of the cart so the hand was placed on the middle and not the end of the cart. The record button was placed and the cart was released.
When the force applied was not positive the data summary was opened and properties icon was pressed for the force sensor and the sign icon was clicked.
The velocity data was checked so that it was smooth. The maximum velocity was to be clearly seen before the motion stopped. One good run was obtained and it was remained two masses. One of the masses was removed from the cart and it was renamed one mass. The masses selection tool was used to display the run for the two masses.
The graph obtained indicated the force against the position which is hook’s law. This is a graph of F against x and it’s a straight line.
The area tool was used to find the area under the graph. The procedure was repeated for the second run.
The run selection tool was used to display the run for the two masses. The maximum velocity of the cart was obtained. The velocity and the cart of the mass were used to calculate the kinetic energy of the cart. This was compared to the elastic cord.
The procedure was repeated for the second run with the masses changed.
Data and ObservationForce for the two masses against time
Time 0 0.1 0.2 0.3 0.4 0.5
Force Mass1 0.0 0.5 1.0 1.5 2.0 2.5
Force Mass2 0.5 1.0 1.5 2.0 2.5 3.0
Velocity of the two masses against time
Time(s) 0 0.1 0.2 0.3 0.4 0.5
Velocity Mass1(m/s) 0.0 0.4 0.9 1.4 1.7 2.0
Velocity Mass 2(m/s) 0.9 1.2 1.4 1.8 2 2.3
Work done by the elastic cord
Time(s) 0 0.15 0.2 0.25 0.3 0.35 0.40
Work done 0 0.5 0.9 1.2 1.5 1.75 1.90
Kinetic energy of the cart
Position (m) 0.1 0.2 0.3 0.4 0.5
Velocity 0.4 0.8 1.1 1.3 1.6
CalculationsVelocity for two masses,
V = 1.36m/s
for the two masses, velocity=1.36ms,W=12mvf2=12×0.754×1.36ms2=1.7J, W=0.307JVelocity for one mass,
V = 1.56m/s
W=12mvf2=12×0.754×1.56ms2=0.917J, W=0.966N/mResultsForce for the two masses against time
Velocity of the two masses against time
Work done by the elastic cord
Kinetic energy of the cart
ConclusionFrom the results obtained from the two exercises, investigating the effect of force on the two masses on the cart and by using the elastic cord, the variation of the kinetic energy of the cart was observed. With variation in the time, the velocity of the cart and the masses increased. In investigating the effect of Hooke’s law, the force applied to the mass attached to the elastic cord was proportional to the displacement of the body. This was evidently expressed graphically from the graph drawn. It was hence observed that the Work Energy Theorem was practically exhibited. The work done by the sum of the forces that were acting on the cart mass was equal to the change in the kinetic energy of the masses.
References BIBLIOGRAPHY Khan. (2010, may). Work energy . Retrieved from Khan Academy.
learning, L. (n.d.). Work Energy theorem. Retrieved from lumenlearning.com: https://courses.lumenlearning.com/boundless-physics/chapter/work-energy-theorem
