Experiment #5: Work and Energy PHY 215-03 GROUP # 4 Alia Barnes Ramon Bing Tiera Johnson Date Conducted: Monday October 7th, 2013
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Purpose & Introduction
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Experimental Details
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Results and Discussion
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Introduction The purpose of experiment #5 is to apply the concept of conservation of energy to determine the work performed by the kinetic frictional force and use the result to determine using energy conservation and the definition of kinetic frictional force. The work done o n an object by a constant force → during s displacement → is given by:
W = → →
(1)
Where is the constant angle between the direction of → → Only the component
of → that is along the displacement → can do work on an object. When a force is applied to an
object resting on a surface, the object will n ot move until the force is greater than the maximum force due to static friction. To keep an object moving at a constant velocity a force must be applied to the object equal to the kinetic frictional force. The kinetic frictional force is determined by the following relation:
(2)
Where is the coefficient for kinetic friction and is the normal force. The average of the four mean force values on the force sensor was used to calculate the height. The symbol for the force sensor is:
(3)
The height of the incline was calculated using the equation:
sin=
(4)
Where is the angle of degrees of the incline, h (cm) is the height of the incline, and L (cm) is the distance traveled. The work done by the motor to slide the block up the incline for each heights, this certain equation was used:
(5)
The equation used to record the blocks gravitational potential energy change for each height was:
(6)
Where is potential energy, m is the mass, g is the gravity, and h is the height. The equation to calculate the work done against friction for each height is
(7)
The equation used to calculate the force of friction from the work relationship and then determining the coefficient of the kinetic friction was:
(8)
where is the frictional force given by:
Experimental Details This lab is dealing with work and how work connects force and force together. In this particular lab the concept of this experiment was to determine the coefficient of kinetic friction for the moving cart using a flat and inclined surface. Formulas were giving in order to solve the tables of kinetic frictional force and work of an object by a constant force during a displacement. Every group was giving a frictional cart and a motorized cart. The motorized cart was used to pull the frictional cart along the tracks. We were to detect the changes in work and energy of the objects. After measuring the mass of the friction cart and 500 gram mass together the Pasco force sensor was joined to the Spark Science Interface. Using a Spark Science Interface attached to the apparatus, the force is measured on a graph. The Spark Science Interface was set up, then each group was to connect the friction cart to the motorized cart making sure the cart was pushed back to zero and pressing the tare button before starting. By using the Spark Science Interface data, the force over the distance of 150 cm was captured. At this step each group member had to intertwine together making sure that the data was consistent. One person would turn on the friction cart and tell the other group member when the friction cart was at 150 cm in order for that group member to record the data on the Spark Science Interface correctly In the first table the trails of the force by the force sensor with different inclines were recorded and averaged. Angle of Trail #1 Trail #2 Trail #3 Trail #4 Force Incline Mean Force Mean Force Mean Force Mean Force averaged over (N) (N) (N) (N) all four trails (N) 0.0 1.53 1.55 1.63 1.49 1.55 5.0 1.80 1.84 1.89 1.86 1.8475 10.0 2.33 2.33 2.28 2.28 2.305 15.0 2.74 2.74 2.71 2.76 2.7375 Table One: Force recorded by the force sensor
In the second table the work, coefficient of kinetic friction, and energy was established and recorded. Using the formulas giving and solved for. Angle of Height Work done by Potential Work of Coefficient of
Incline (°)
(of 150 cm mark)
motorized Energy cart Change W motor_cart ΔPE 0.0 0 2.325 0 5.0 .1307 2.77125 .765954 10.0 .2605 3.4575 1.5266342 15.0 .3882 4.1065 2.275007 Table Two: Work, Energies, and Coefficient of Kinetic Force
Friction Force W friction 2.325 2.005296 1.9308 1.8314
kinetic friction μk 25.401 21.71 20.77 19.326
Results/ Discussion Angle of Trial #1 Trial #2 Incline Mean Force Mean Force (°) (N) (N) 0.0 1.53 1.55 5.0 1.80 1.84 10.0 2.33 2.33 15.0 2.74 2.74 Table One: Force recorded by the force sensor
Trial #3 Mean Force (N) 1.63 1.89 2.28 2.71
Angle of Height, h Work done by Potential Incline (m) motorized cart Energy Change (°) (J) (J) 0.0 0 2.32 0 5.0 .130 2.77 .765 10.0 .260 3.45 1.52 15.0 .388 4.10 2.27 Table Two: Work, Energies, and Coefficient of Kinetic Force
Trial #4 Mean Force (N) 1.49 1.86 2.28 2.76
Force averaged over all four trials (N) 1.55 1.84 2.30 2.73
Work of Friction Force (N) 2.32 2.00 1.93 1.83
Coefficient of kinetic force (μ) 25.40 21.71 20.71 19.32
In order to calculate the results in Table One and Two, the mass of the friction cart should be converted from 598 grams to .598 kilograms. The measurements for the length of the flat track were also converted from 150 centimeters to 1.50 meters. Work refers to an activity involving a force and the movement in the direction of the force; work was completed by the motorized cart. Energy is the capacity for completing work; in order to do work, one must have energy. Potential energy is the energy that is stored and possessed by an object. The potential energy change was calculated. Kinetic energy is associated with motion; an object has kinetic energy due to its motion. The work completed by the motorized cart was calculated by multiplying the force average by 1.50 meters. The potential energy change was calculated by multiplying the total mass of the friction cart, gravity, and the height of each angle of incline, or shown as: Δ . The work of friction force was calculated by subtracting the work of the motorized cart and the potential energy change, or shown as: Δ . The results for the coefficient of kinetic force were calculated by
. The
total mass of the friction cart was multiplied by gravity and cosine of the angle and divided by the friction force.
Conclusion A frictional cart that was pulled along a track was used to observe changes in work and energy. Additionally, a motorized cart was used that was able to pull the frictional cart at a constant velocity. In order to measure the applied force, a Pasco force sensor that is attached to a Spark Science Interface. The experiment was a success in measuring the effect of friction on the motion and energy of the sliding cart. The sliding cart was also measured at different angles of the track incline. The total mass of the friction cart and load was measured to be .598 kilograms. With each incline of the track at higher angles, the mean force recorded rose with each of the four trials. After each of the trials was completed, the force average over all of the four trials was calculated as well. At a zero degree angle, the average force for all four trials was calculated to be 1.55 Newtons. Next, at a five degree angle, the average force for all four trials was calculated to be 1.84 Newtons. For an angle of ten degrees, the average force for all four trials was calculated to be 2.35 Newtons. Lastly, for an angle of fifteen degrees, the average force for all four trials was calculated out to be 2.73 Newtons. Table two shows the calculated work, energies, and coefficient of Kinetic Force. In order to calculate the height for each of the angles, 1.50 meters was multiplied by the function, sine and each angle degree. The work completed by the motorized cart was calculated by multiplying the force average by 1.50 meters. The potential energy change was calculated by multiplying the total mass of the friction cart, gravity, and the height of each angle of incline. The work of friction force was calculated by subtracting the work of the motorized cart and the potential energy change. The coefficient of kinetic force was able to be calculated by dividing the mass, function of cosine of the angle by the Friction force. The experiment was successful in the determination of the coefficient of kinetic force for a sliding cart on a flat track, as well as inclined. If there were any source of error involved in the laboratory technique, the error woul be in computations. The Spark Science Interface was used to calcualte the means in each trial. In order to properly calculate the data, one had to turn the data on and off while the cart was still moving. If this was not done, the results would not be accurate.
References [1] Introductory Physics II, PHY-215, Laboratory #5 Work and Energy, Dept of Physics, Hampton University, 2012.
