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 travelled 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 first need to find the time it takes for the glider to travel the distance of 96 cm.
Using the given information, we can calculate the velocity of the glider using the formula:
v = d/t
where v is the velocity, d is the distance, and t is the time.
v = 96 cm / 333 ms
v = 0.288 meters per second (m/s)
Next, we can find the time it takes for the glider to travel the length of 8.0 cm. Since acceleration is assumed to be constant, we can use the formula:
v = u + at
where u is the initial velocity (which is 0 m/s since the glider is released from rest), a is the acceleration, and t is the time.
Rearranging the formula, we have:
t = (v - u) / a
t = 0.333 s
Now, we can solve for the acceleration:
a = (v - u) / t
a = (0.288 m/s - 0 m/s) / 0.333 s
a ≈ 0.864 meters per second squared (m/s²)
Therefore, the acceleration of the glider along the track is approximately 0.864 m/s².