Consider a mass placed on top of the rotating turntable at a distance of 12 cm. The speed of the turntable was gradually increased until the mass just slid off. New assume that the time interval between the last two photogate spikes was 0.16 sec. calculate the tangential speed of the mass
To calculate the tangential speed of the mass, we need to know the distance traveled by the mass in the time interval between the last two photogate spikes.
Given:
Distance from the center of the turntable to the mass (r) = 12 cm = 0.12 m
Time interval between the last two photogate spikes (t) = 0.16 s
The distance traveled by the mass on the turntable can be calculated using the formula:
Distance = Speed × Time
To find the tangential speed, we rearrange the formula:
Speed = Distance / Time
Since the mass just slid off the turntable, we can assume that the distance traveled by the mass is equal to the circumference of the circular path it was on.
Circumference = 2πr
Now we can substitute the values and calculate the tangential speed:
Speed = (2πr) / t
= (2 × 3.14 × 0.12) / 0.16
≈ 2.36 m/s
Therefore, the tangential speed of the mass is approximately 2.36 m/s.