posted by rm .
In an arcade game a 0.142 kg disk is shot across a frictionless horizontal surface by compressing it against a spring and releasing it. If the spring has a spring constant of 174 N/m and is compressed from its equilibrium position by 8 cm, find the speed with which the disk slides across the surface. Answer in units of m/s
Fs = 174 N/m * 0.08 m = 13.92 N. = Force of the spring.
a = Fs/m = 13.92 / 0.142 = 98 m/s^2. =
acceleration of the arcade game.
d = at^2 = 0.08 m.
98t^2 = 0.08,
t^2 = 0.000816,
t = 0.02857 s.
V = at = 98 * 0.02857 = 2.8 m/s.
Henry's equation d = at^2
is not correct, but there may be a compensating error somewhere else, such as in assuming constant acceleration. I get the same answer, however.
I prefer to use conservation of energy.
Stored spring potential energy
= kinetic energy when released
(1/2) k d^2 = (1/2) m V^2
V = d sqrt (k/m) = 0.08*sqrt(174/0.142)
= 2.8 m/s