Materials: None 
Time Allotment: 5 Class Days 
This makeup lab is unique from most others in that it does not actually involve a laboratory exercise. Rather, this makeup lab involves the completion of two mathematical analyses which demonstrate your understanding of the relationship between work and energy changes. In this activity, you will use freebody diagrams, kinematic equations, vector principles, and work and energy concepts to analyze two of physical situations in which work is done upon an object in order to change the mechanical energy of the object.
The wealth of mathematical relationships which you will need to use to complete the analyses in this activity are identified below.
For an object with a constant acceleration (a), the displacement (d), time (t), intial velocity (vi) and final velocity (vf) are related by the following equations:
vf = vi + a*t
d = [(vi + vf)/2]*t
vf^2 = vi^2 + 2*a*d
d = vi*t + 0.5*a*t^2
The acceleration of an object (a) is related to the net force (F_{net}) acting upon the object. The net force is merely the vector sum of all the individual forces acting upon the object. The net force can often be found using a freebody diagram analysis. Individual forces such as the force of gravity (F_{grav}) and the force of friction (F_{frict}) have special equations.
F_{net} = m*a
F_{grav} = m*g
F_{frict} = mu*F_{norm}
where m = mass, g = acceleration of gravity, mu = coefficient of friction
An object on an inclined plane experiences a force of gravity which can be resolved into two components  one parallel to the incline and one perpendicular to the incline.
F_{parallel} = m*g*sin(Theta)
F_{perpendicular} = m*g*cos(Theta)
where m = mass, g = acceleration of gravity, Theta = incline angle
The mechanical energy possessed by an object can be in the form of either kinetic energy (KE) or potential energy (PE).
KE = 0.5*m*v^2
PE = m*g*h
where m = mass, v = velocity, g = acceleration of gravity, h =height
Work done (W) by an external force (F) can change the mechanical energy of an object. The rate at which work is done is referred to as the power (P). The power output can be determined by one of the following equations:
P = F*d*cos(Theta)/t
P = F*v
where m = mass, d = displacement, v = velocity, t = time, Theta =angle between F and d
Further information is available at The Physics Classroom.
A 60kg skier is pulled at constant speed up a hill by a toe rope at varying incline angles to the same height of 30 meters. In each case, the force pulling on the skier is parallel to the hill. If it is assumed that friction and air resistance forces are negligible due to the icy surface and the low speeds, then the force of the toe rope on the skier balances the parallel component of the weight vector.
For the varying incline angles listed in the tables below, determine the force applied to the skier, the displacement of the skier from the bottom of the hill to the 30meter summit (using trigonometric relationships), the work done on the skier, and the potential energy change of the skier. Show your work for the first row of each data table.
Incline Angle (degrees) 
Force applied to skier (N) 
Displacement (m) 
Work Done on Skier (J) 
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Incline Angle (degrees) 
Mass of Skier (kg) 
Height of Hill (m) 
PE Change of Skier (J) 
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Compare the work done on the skier by the toe rope to the potential energy change of the skier. What conclusions can you draw?
If a 1horsepower motor (approximately 750 Watts) is used to toe the skiers up the hill, then determine the time which would be required to toe them to the top of each hill and the velocity at which they would be toed. (Use the work and displacement values determined in the tables above). Show your work for the first row of each data table.
Incline Angle (degrees) 
Velocity of Skier (m/s) 
Time to reach top (s) 
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A rightwardmoving 800kg sports car is skidding to a stop across a horizontal roadway. The coefficient of friction between the tires and the road surface is 0.90. Draw a freebody diagram (showing the direction and types of forces acting upon the car) and determine the car's acceleration as it skids to a stop.
For the varying values of the initial velocities given in the table below, use a kinematic equation to determine the displacement of the car during its skid. Use a work equation to determine the work done by friction upon the 800kg car. Use the kinetic energy equation to determine the kinetic energy change of the car. Show your work for the first row of each data table.
Initial Velocity (m/s) 
Displacement (d) 
Work Done (J) 
KE Change of Car (J) 
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Compare the work done on the car by friction to the kinetic energy change of the car. What conclusions can you draw?
Write a conclusion in which you define work and explain the relationship between the work done on an object by an external force and the mechanical energy change of the object. Give one concrete example of your own to illustrate your explanation. Do a bangup job.
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This page created by Tom Henderson and last updated on 12/4/97.