A 1.3-kg model airplane flies in a circular path on the end of a 23-m line. The plane makes 4.3 revolutions each minute.
a. What is the period of the motion?
b. What is the speed of the plane?
c. What is the acceleration of the model plane?
d. How much force must the line exert on the plane to keep it moving in the circular
motion?
To find the answers to these questions, we need to use some principles from physics.
a. The period of motion is the time it takes for one full revolution. It can be calculated by taking the inverse of the frequency (the number of revolutions per second). In this case, the plane makes 4.3 revolutions per minute, so the frequency is 4.3/60 Hz (since there are 60 seconds in a minute). To find the period, we take the inverse of the frequency:
Period = 1 / Frequency
b. The speed of the plane can be calculated using the formula:
Speed = 2πr / Period
where r is the radius of the circular path (length of the line) and Period is the time for one full revolution (which we found in part a).
c. The acceleration of the model plane can be determined using the formula:
Acceleration = (Velocity^2) / Radius
where Velocity is the speed of the plane (which we found in part b) and Radius is the length of the line.
d. In order to keep the plane moving in a circular motion, the line must exert an inward force called the centripetal force. This force can be calculated using the formula:
Force = Mass * Acceleration
where Mass is the mass of the model airplane (given as 1.3 kg) and Acceleration is the acceleration of the model plane (which we found in part c).
Now, let's calculate the answers step by step:
a. The period of motion is given by:
Period = 1 / (4.3/60) = 60 / 4.3 seconds
b. The speed of the plane is given by:
Speed = (2π * 23) / (60 / 4.3) = 2π * 23 * (4.3/60) m/s
c. The acceleration of the model plane is given by:
Acceleration = (Speed^2) / 23 m/s^2
d. The force exerted by the line to keep the plane in circular motion is given by:
Force = Mass * Acceleration
Plug in the given values to find the force.
Please note that any numerical values given above are just for explanation purposes and may not represent actual values in this specific scenario.