Brown University
Department of Physics
Physics 50/70
Handout (L-5)
Acceleration of a Body Down An Inclined Plane
In this experiment we calculate the expected acceleration by use of Newton’s laws, and
then measure the acceleration as in handouts L-3A and L-4 for comparison.
1. Theory:
Newton’s second law is


F  ma
(1)

Where, F is the vector sum or resultant of all forces applied, m is the mass of the body

upon which the forces act, and a is the resultant vector acceleration.
As the body of mass m we use (Fig. 1) the glider of an air track which is inclined at an
angle  with respect to the horizontal. Three forces, shown as solid—line vectors, act on



the-body; Its own weight F  mg ; the normal force N , perpendicular to the “plane”,

which is exerted by the air track (through the cushion of air); and f , a frictional force.


Thanks to the air track, f is so small that it can be neglected entirely. (However, f could
easily be included in the analysis if its value is known.)
θ
Fig1. The Setup of the Inclined Plane Experiment

It is convenient to resolve F into its components F1 along the line of N and F2 along the
131126
1
Brown University
Department of Physics
Physics 50/70
Handout (L-5)

“plane” (and hence along the line of f ). These components are shown in dotted line; note
that F itself should now be removed from the diagram, because its components F1 and F2
replace it. It is physically obvious that no acceleration occurs along the line of N and F1,
N  F1  N  F cos  mg sin 
Along the only allowed direction of motion, the resultant force is F2  f :
F2  f  F2  F sin   mg sin 
(2)


Now the glider’s acceleration a can be computed. Clearly a is in the direction of F2,

which f being negligible——is the resultant of all forces acting on the body.
2. Procedure:
There are several methods available to measure the glider acceleration.
(1) Use photogate timers to calculate the glider acceleration (See handout L-3A for a
discussion of the air track and photogate timer)
(2) use a tape timer to measure the glider acceleration (See handout L-4 for a discussion
of the tape timer)
(3) Use motion sensors to measure the glider acceleration (see Pasco Data Studio manual
for more information)
(4) Use a video camera and Tracker computer software to measure the glider acceleration
(see http://www.youtube.com/watch?v=R1dKhRBNmCU or Handout L-6 Motion in Two
Dimensions for further discussion). You must first capture video using VirtualDub, save
as .avi, and then open video in Tracker.
Below we outline the tape timer method for calculating the acceleration.
Weigh the glider on a pan balance. Put a riser block, at least 2 inches high, under one end
of the track, and calculate the resulting value of sin ; mark this value on the timer tape.
Also, estimate the accuracy of determining sin . Attach the timer tape securely to the
glider.
Release the glider at the upper end of the track, turning on the tape timer simultaneously.
Turn off the tape timer just as the glider reaches the bumper, to avoid getting extra tape
timer points upon rebound.
131126
2
Brown University
Department of Physics
Physics 50/70
Handout (L-5)
Repeat the run with two other riser blocks, always exceeding 2 inches.
On each tape, choose a point t = 0 (Handouts L3A, L4); measure and tabulate successive
distances s (always from the point “t=0”). By any of the methods in handout L-4,

determine a for each angle  and compare with the expected value. Since a constant
acceleration is predicted dynamically, you may omit the parts of handout L-3A devoted
to establishing this fact, although some of the specific methods prove this constancy
automatically. The value of v0 is not needed here.
3. Question: (to be answered in your report)

1. If a and sin are known; this experiment offers a rather indirect way of determining g
(Galileo proceeded somewhat similarly by rolling spheres down an incline, but the
rotational motion greatly complicates the analysis). From your three runs, determine a
value of g, estimate its precision, and compare with the known value.
2. From the dynamical equations and your results, estimate the maximum possible value
that the frictional force could have had.
131126
3