A spring scale on a rotating platform indicates that the horizontal force on a 0.681 kg mass is 1.48 N when the mass is 2.62 m from the axis of rotation. How long does it take for the platform to make one revolution?
To find the time it takes for the platform to make one revolution, we need to first calculate the angular velocity of the platform.
The torque exerted on the mass can be found using the formula:
Torque = force × distance
The torque acting on the mass is provided by the spring scale and is given by the equation:
Torque = mass × acceleration × distance
In this case, the torque is equal to the force provided by the spring scale multiplied by the distance from the axis of rotation. Therefore:
mass × acceleration × distance = force × distance
Simplifying the equation, we have:
mass × acceleration = force
Now we can find the acceleration:
acceleration = force / mass
Using the given values:
acceleration = 1.48 N / 0.681 kg
Next, we can find the angular acceleration of the platform:
angular acceleration = acceleration / distance
angular acceleration = (1.48 N / 0.681 kg) / 2.62 m
Now, we can use the equation for rotational motion:
angular acceleration = change in angular velocity / time
Since the platform is completing one revolution, the change in angular velocity is equal to 2π radians. Therefore:
(1.48 N / 0.681 kg) / 2.62 m = (2π radians) / time
Simplifying the equation, we can solve for time:
time = (2π radians) × (0.681 kg × 2.62 m) / 1.48 N
Evaluating the expression:
time = (2π) × (0.681 × 2.62) / 1.48
Finally, we can calculate the value of time:
time ≈ 7.38 seconds
Therefore, it takes approximately 7.38 seconds for the platform to make one revolution.