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 velocity
To calculate the tangential velocity, we need to find the distance covered by the mass in the given time interval.
Given:
Distance from the center of rotation to the mass (r) = 12 cm = 0.12 m
Time interval (Δt) = 0.16 s
The distance covered by the mass can be calculated using the formula:
Distance = Tangential Velocity × Time
Let's assume the tangential velocity is V.
Distance = V × Δt
Since the mass just slid off, the distance covered by the mass is equal to the circumference of the turntable at the location of the mass.
Distance = Circumference
The circumference of a circle can be calculated using the formula:
Circumference = 2πr
Plugging in the given values:
0.12 m = 2πr
Solving for the circumference:
Circumference = 2π(0.12 m)
Circumference = 0.24π m ≈ 0.75398 m
Setting the distance covered by the mass equal to the circumference:
V × Δt = 0.24π m
Solving for the tangential velocity:
V = 0.24π m / Δt
Plugging in the given time interval:
V = (0.24π m) / (0.16 s)
Calculating the tangential velocity:
V ≈ 1.5 m/s