An air track glider, 8.0 cm long, blocks light as it goes through a photocell gate. The glider is released from rest on a frictionless inclined track and the gate is positioned so that the glider has traveled 96 cm when it is in the middle of the gate. The timer gives a reading of 333 ms for the glider to pass through this gate. Friction is negligible. What is the acceleration (assumed constant) of the glider along the track?
To find the acceleration of the glider along the track, we can use the kinematic equation:
s = ut + (1/2)at^2
where:
s = displacement (96 cm)
u = initial velocity (0 cm/s since the glider is released from rest)
t = time taken (333 ms, which is equivalent to 0.333 s)
a = acceleration (unknown)
First, let's convert the given quantities to SI units:
s = 96 cm = 0.96 m
u = 0 cm/s = 0 m/s
t = 0.333 s
Now we can substitute the values into the equation and solve for acceleration:
0.96 m = (0 m/s)(0.333 s) + (1/2)a(0.333 s)^2
Simplifying the equation:
0.96 = 0 + (1/2)a(0.111 s^2)
0.96 = (1/2)(0.111 s^2)a
Multiplying both sides of the equation by 2 and dividing by 0.111 s^2:
(2 * 0.96) / (0.111 s^2) = a
a ≈ 17.12 m/s^2
Therefore, the acceleration of the glider along the track is approximately 17.12 m/s^2.