At our university, students in introductory physics classes perform a laboratory exercise to measure the range of a projectile fired at an assigned angle. A set of photogates is used to determine the initial velocity of the projectile (the launch velocity). We noticed a systematic deviation between the experimentally measured range and the range calculated using the speed as determined by the photogates. In this paper, we will discuss the origin of this systematic error and derive a simple formula to correct it. In particular, we find that the launch speed given by our instrument is significantly different from the actual launch speed of our projectile.
REFERENCES
1.
PASCO Projectile Launcher (ME-6825) and two Photogates (ME-9498B). To hold the photogates, we use the Pasco Mounting Bracket (ME-6821A).
2.
2. PASCO ScienceWorkshop 750 Interface and Pasco DataStudio software, version 1.9.0.
3.
See, for example,
D.
Halliday
, R.
Resnick
, and J.
Walker
, Fundamentals of Physics
, 9th ed. (Wiley
, Hoboken, NJ
, 2011
), p. 122
.4.
J. W.
Schnick
, “Projectile motion details,”
Phys. Teach.
32
, 266
–269
(May 1994
).5.
J. G.
Winans
, “Convenient equations for projectile motion,”
Am. J. Phys.
29
, 623
–626
(Sept. 1961
).6.
R.
Vesecky
, “Solving the trajectory problem without trigonometry,”
Phys. Teach.
8
, 263
–265
(May 1970
).7.
H. L.
Armstrong
, “Comment on trajectories without trigonometry,” letter to the editor
, Phys. Teach.
9
, 41
–42
(Jan. 1971
).8.
P.
Lucie
, “Projectile motion revisited,”
Am. J. Phys.
47
, 139
–141
(Feb. 1979
).9.
P.
Palffy-Muhoray
and D.
Balzarini
, “Maximizing the range of the shot put without calculus,”
Am. J. Phys.
50
, 181
(Feb. 1982
).10.
S. K.
Bose
, “Maximizing the range of the shot put without calculus,”
Am. J. Phys.
51
, 458
–459
(May 1983
).11.
H. L.
Armstrong
, “Another treatment of a trajectory,”
Am. J. Phys.
51
, 1146
(Dec. 1983
).12.
S. K.
Bose
, “Thoughts on projectile motion,”
Am. J. Phys.
53
, 175
–176
(Feb. 1985
).13.
P. A.
Macklin
, “Projectile motion maxima—An omnipresent orthogonality,”
Am. J. Phys.
55
, 947
(Oct. 1987
).14.
J. C.
Moore
, J. C.
Baker
, L.
Franzel
, D.
McMahon
, and D.
Songer
, “Graphical method for determining projectile trajectory,”
Phys. Teach.
48
, 61
–613
(Dec. 2010
).15.
Equation (7) was derived assuming that the first photogate was at the launch point. If that is not the case, and the first photo-gate is a distance l from the launch point, then an additional correction is required. If the result of Eq. (7) is denoted , then the correct launch speed is . for our apparatus mm or less, and the difference between and is at most 0.5%.
© 2013 American Association of Physics Teachers.
2013
American Association of Physics Teachers
AAPT members receive access to The Physics Teacher and the American Journal of Physics as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.