A model airplane whose mass is 875 grams flies in a horizontal circle of radius 3.46 m at the end of a string which is at an angle of 10.5o below the horizontal. Find:
a) The tension in the string.
b) The speed of the airplane.
I have answers but I am stuck on the process like what to use.
mg = Tsinα
T=mg/sinα=0.875•9.8/sin10.5 =0.817 N
mv²/R = Tcosα
v=sqrt{TRcosα/m} =
=sqrt{0.817•3.46cos10.5/0.875} = 1.78 m/s
To solve this problem, we can start by finding the tension in the string and then use that result to find the speed of the airplane.
a) To find the tension in the string, we need to consider the forces acting on the airplane. The tension in the string is the centripetal force that keeps the airplane moving in a circle.
Since the airplane is flying in a horizontal circle, the vertical component of the tension is equal to the weight of the airplane, which can be calculated as:
Weight = mass * gravity
Where the mass of the airplane is given as 875 grams (0.875 kg) and the acceleration due to gravity is 9.8 m/s^2.
Weight = 0.875 kg * 9.8 m/s^2
Next, we need to find the horizontal component of the tension, which acts as the centripetal force. We can use the following equation:
Centripetal force = Mass * (Velocity)^2 / Radius
Where the mass of the airplane is 0.875 kg and the radius of the circle is given as 3.46 m.
Now, we can solve for the tension by setting the vertical component of the tension equal to the weight:
Vertical component of tension = Weight
And the horizontal component of the tension equal to the centripetal force:
Horizontal component of tension = Centripetal force
b) To find the speed of the airplane, we can use the following equation:
Speed = (Angular velocity) * Radius
Where the angular velocity can be calculated as:
Angular velocity = (2 * π * Frequency) / 360
Given that the angle relative to the horizontal is 10.5 degrees, we can find the frequency:
Frequency = 360 / Angle
Once we have the angular velocity, we can substitute it into the speed equation along with the given radius.
Now, by following these steps, you can calculate the answer for parts (a) and (b) of the problem.