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Mechanical Energy
In today’s laboratory, we will be examining the effect of non-conservative forces on an object. When
only a conservative force, such as gravity, acts on an object, energy is converted from potential to
kinetic energy (or vice-versa), but the total mechanical energy remains the same. A non-conservative
force, such as friction, acting on an object will cause a change in the mechanical energy. We will be
sliding a cart down an inclined plane and measuring the change in mechanical energy caused by
friction.
The mechanical energy of a system is defined as the sum of the potential and kinetic energies:
E = KE + U = 21 m v 2 + m g h
When only conservative forces act on an object, this sum is always a constant; mechanical energy
is conserved. However, when a non-conservative force acts on the object, the mechanical energy is
changed by the amount of work done by the non-conservative force, as per the work energy theorem:
If the non-conservative force is friction, the applied force acts in the opposite direction to the
Wnc = ∆ E = ∆ KE + ∆U
displacement, so the work done by friction is:
Wnc = - Ff d
The mechanical energy is converted into thermal energy of the system.
Experimental Set-up
Begin the experiment with the track lying flat on the table.
Pull down the Setup -> Data Collection menu, and confirm that the Experiment Length is set at 2
seconds, the Sampling Rate at 40 samples/second, and the Averaging is set to none. Zero the force
meter when there is no tension on the line.
You will be rolling a cart down the inclined track to look at the effect of the non-conservative
frictional force. The friction between the track and the cart will be supplied by taping a paper
towel to the bottom of the cart. Make sure that it provides enough friction to cause a significant
change in the motion, but not so much friction that the cart has trouble moving. In order to find
the force of friction.
Part 1: Frictional Forces
We begin with a study of the frictional force. Eventually we are interested in determining the
coefficient of kinetic friction.
If you try to slide a heavy box resting on the floor, you may find it difficult to get the box moving.
Static friction is the force that is acting against the box. If you apply a light horizontal push that
does not move the box, the static friction force is also small and directly opposite to your push. If
you push harder, the friction force increases to match the magnitude of your push. There is a
limit to the magnitude of static friction, so eventually you may be able to apply a force larger
than the maximum static force, and the box will move. The maximum static frictional force is
sometimes referred to as starting friction. We model static friction, Fstatic , with the inequality
Fstatic ≤ µ s N , where µs is the coefficient of static friction and N is the normal force exerted by
a surface on the object.
Once the box starts to slide, you must continue to exert a force to keep the object moving, or
friction will slow it to a stop. The frictional force acting on the box while it is moving is called
kinetic friction. In order for the box to slide with a constant velocity, a force equivalent to the
force of kinetic friction must be applied. Kinetic friction is sometimes referred to as sliding
friction. Both static and kinetic friction depend on the surfaces of the box and the floor, and on
how hard the box and floor are pressed together. We model kinetic friction with Fkinetic = µ k N ,
where µk is the coefficient of kinetic friction.
In this experiment, you will use a Force Sensor to study static friction and kinetic friction on the
cart. When the cart is pulled along the track at a constant speed, the tension in the line is equal
in magnitude to the frictional force. Find the mass of the cart.
Tie one end of a string to the hook on the Force Sensor and the other end to the hook on the cart.
Practice pulling the block and masses with the Force Sensor using this straight-line motion.
Slowly and gently pull horizontally with a small force. Very gradually, taking one to two full
seconds, without taking any data, increase the force until the cart starts to slide, and then keep
the cart moving at a constant speed for another second.
Open the experiment file "Friction" in Logger Pro. Hold the Force Sensor in position, ready to pull
the block, but with no tension in the string. Click on the Zero button at the top of the graph to set
the Force Sensor to zero. Click
to begin collecting data. Pull the block as before, taking
care to increase the force gradually. Repeat the process as needed until you have a graph that
reflects the motion, including pulling the block at constant speed once it begins moving.
Compare the force necessary to start the block sliding to the force necessary to keep the block
sliding. The coefficient of friction is a constant that relates the normal force and the force of
friction. Would you expect the coefficient of static friction to be greater than, less than, or the
same as the coefficient of kinetic friction?
Examine the data by clicking the Statistics button. The maximum value of the force occurs when
the block started to slide. Read this value of the maximum static frictional force from the floating
box and record the number in your lab report. Drag across the region of the graph corresponding
to the block moving at constant velocity. Click on the Statistics button again and read the
average force during this time interval, and record it in your lab report. This force is the
magnitude of the kinetic frictional force.
Repeat the above procedure twice more, adding masses of 300 and 500 g to the cart. For each
case draw a free body diagram of the block while it is not being pulled at all. Use Newton's
second law to determine the normal force on the block. Find the average values of
µ k and µ s.
Part 2: Work of non-conservative forces
Set the end of the track on the metal crossbar, and align the motion detector so that it points directly
down the plane. Use the knobs on the bottom side of the track to ensure that the track does not
slide off the bar. Measure the angle made by the track and the table with a protractor. Remove the
line and the masses from the cart and set it on the track so that the sail is just beyond 40 cm from
the motion detector. (This is the lower limit of the detector’s range.) Mark the position of the lower
end of the cart on the track in this position. Calculate the mechanical energy of the cart at this point.
How far down the track can the cart slide? In the absence of friction, what would the mechanical
energy of the cart be when it reached that point? What would its speed be?
Calculate the force of friction on the cart. Remember that since the cart is on an incline, the normal
force is not simply the weight. Draw a free body diagram to help you see this. Over what distance does
the frictional force act? Calculate the work done by friction over this distance. Is this work positive
or negative? Use the work energy theorem to calculate the mechanical energy at the bottom of the
track, taking friction into account. Predict the speed of the cart at the bottom.
Set the cart at the point you marked at the top of the incline, press Collect, and let the cart slide
down the track. Record the speed when the cart reaches the bottom. Repeat this three more times,
always using the same starting position. Find the mean value for the final speed, and the average
deviation from the mean. Find the percent difference between the mean value and your calculated
value. (Use the calculated value in the denominator.) Give some possible reasons for the difference
between the two values.
If the mass of the cart increases, will the speed at the bottom change? Repeat the experiment,
adding masses of 100 and 200 g to the cart. (Only do one trial for each.)