Newton's First and Third Laws
Read the sections of your lecture textbook dealing with Forces,
Free-body Diagrams, and Newton's Second and Third Laws.
Rules for Drawing Free-body Diagrams
- Draw each object in isolation, that is, floating in space with no
other objects in the picture.
- Attach only forces which act on the object, not forces which
the object under consideration applies to other objects.
- The weight force always points down (toward the center of the Earth)
and always has magnitude mg.
- The normal force can only push, not pull, perpendicular to the surface.
- The string tension force can only pull along the direction of the string.
- The friction force acts parallel to the surface, in a direction opposite
to the velocity vector of the object.
- Forces act on one object and are caused by one object.
- An object can not exert a force on itself.
- Action-reaction partner forces never act on the same object.
- Action-reaction partner forces always have the same cause, that is, if
one is gravitational then the other is gravitational; if
one is normal then the other is normal.
- Add a 200-gram load to the cart and measure the total mass using
a triple beam balance at the
instructor's desk. Include units and an error estimate.
- Multiply the mass of the loaded cart by g to calculate its
weight. (g = 9.80 m/s2 ± 0.01 m/s2)
- Set the angle of the incline to 15o. The bottom of the
indicator should be aligned to the angle mark.
- Tie a cord to the cart, pass the cord over the pulley, and
attach a weight hook to the cord.
- The pulley should be extended as far as possible along its rod so
that at the largest angles the vertical string is able to clear the
- Adjust the pulley to make the cord parallel to the slope. (Why?)
- Add sufficient slot masses to the hook to achieve a rough
equilibrium. It is not necessary to record this rough mass.
- Using slot masses as small as 1 gram, adjust the hanging mass
so that the cart will move up the slope at a very slow constant
speed (zero acceleration). For the error in the mass on the hanger,
estimate how much mass must be added or subtracted to the hanger
before you notice a difference in the behavior of the cart.
- Record the slope angle and the amount of hanging mass. Note that the
hook itself has a mass of 50 grams.
- Readjust the hanging mass so that the cart will move down the
slope at a very slow constant speed (zero acceleration). Record
this new hanging mass.
- Calculate the average hanging mass from the up and down trials.
- Find the average tension in the cord at this angle from the average
mass (upward and downward motion).
- Repeat for slope angles 20o, 25o,
... , 45o (or as large as feasible).
- It is possible that at the lowest angle 15o, the empty hanger
itself may be too heavy to allow the cart to move down the ramp at
constant speed. If this is the case, omit the data point at
- Why is it necessary that the cord be parallel to the slope?
- Why is it necessary to roll the cart at constant speed?
- Why is it necessary to roll the cart both up and
down the slope?
- Draw a free-body diagram for the cart. Determine from theory
the tension required to achieve equilibrium as a function of angle.
- Plot the measured average string tension T (vertical axis) vs.
the angle of inclination
(horizontal axis). Compare this to the curve predicted from theory.
The data should appear as points; the theory should be a solid curve.
Do not fit the data points by eye; do not draw the best straight line
though the data (they do not lie on a straight line). Simply plot the
data and theory on the same set of axes and observe how closely they
- Calculate the propagated error on the tension for each angle. Are the
error bars on your plotted data points visible on this graph, or are
they too small to be seen?
- The first student to email me (Dr. Scalise) with the
correct answer to the following question will receive 10 points added
to their final exam grade. What is the sum of the prime numbers
between 1 and 110? It pays to read the labs carefully in advance.
(Do not email. This question has already been answered for
Fall 2010. The answer was sent on 24 September 2010.)
- Identify at least two sources of statistical error.
- Identify at least two sources of systematic error.
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