Question

Problem 2 A model airplane of mass $m = 0.750$ kg flies with a constant speed $v = 35.0$ m/s in a horizontal circle at the end of a control wire of length $L = 60.0$ m as shown in the figure below. The aerodynamic lift force $F_{lift}$ (shown in the figure) acts at angle $ heta = 30^circ$ inward from the vertical, and the wire makes the same constant angle $ heta$ with the horizontal. Circular path of airplane $F_{lift}$ $ heta$ Wire a $ heta$ Wire b Figure 8: Problem 2. (a) Draw and label all other forces acting on the airplane. Indicate the direction of the acceleration. (3pt) (b) What is the radius of the circular path of the airplane? (3pt) (c) What is the magnitude of the airplane's centripetal acceleration? (3pt) (d) Find the tension in the wire and the magnitude of the lift force. (11pt) Bonus: What is the period of one revolution? How many revolutions per one minute does the airplane make? (3pt)

          Problem 2
A model airplane of mass $m = 0.750$ kg flies with a constant speed $v = 35.0$ m/s in a
horizontal circle at the end of a control wire of length $L = 60.0$ m as shown in the figure
below. The aerodynamic lift force $F_{lift}$ (shown in the figure) acts at angle $	heta = 30^circ$ inward
from the vertical, and the wire makes the same constant angle $	heta$ with the horizontal.
Circular path
of airplane
$F_{lift}$
$	heta$
Wire
a
$	heta$
Wire
b
Figure 8: Problem 2.
(a) Draw and label all other forces acting on the airplane. Indicate the direction of the
acceleration. (3pt)
(b) What is the radius of the circular path of the airplane? (3pt)
(c) What is the magnitude of the airplane's centripetal acceleration? (3pt)
(d) Find the tension in the wire and the magnitude of the lift force. (11pt)
Bonus: What is the period of one revolution? How many revolutions per one minute does
the airplane make? (3pt)

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Problem 2
A model airplane of mass m = 0.750 kg flies with a constant speed v = 35.0 m/s in a
horizontal circle at the end of a control wire of length L = 60.0 m as shown in the figure
below. The aerodynamic lift force Flift (shown in the figure) acts at angle heta = 30^circ inward
from the vertical, and the wire makes the same constant angle heta with the horizontal.
Circular path
of airplane
Flift
heta
Wire
a
heta
Wire
b
Figure 8: Problem 2.
(a) Draw and label all other forces acting on the airplane. Indicate the direction of the
acceleration. (3pt)
(b) What is the radius of the circular path of the airplane? (3pt)
(c) What is the magnitude of the airplane's centripetal acceleration? (3pt)
(d) Find the tension in the wire and the magnitude of the lift force. (11pt)
Bonus: What is the period of one revolution? How many revolutions per one minute does
the airplane make? (3pt)

Added by Amy H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Timothy James

07/12/2022

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96 \text{ meters} \] ** Show more…

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A model airplane of mass m = 0.750 kg flies with a constant speed v = 35.0 m/s in a horizontal circle at the end of a control wire of length L = 60.0 m as shown in the figure below. The aerodynamic lift force F_lift (shown in the figure) acts at an angle ̈́Θ = 30° inward from the vertical, and the wire makes the same constant angle Θ with the horizontal. Circular path of airplane Wire Wire Figure 8: Problem 2 (a) Draw and label all other forces acting on the airplane. Indicate the direction of the acceleration. (3pt) (b) What is the radius of the circular path of the airplane? (3pt) (c) What is the magnitude of the airplane's centripetal acceleration? (3pt) (d) Find the tension in the wire and the magnitude of the lift force. (11pt) Bonus: What is the period of one revolution? How many revolutions per one minute does the airplane make? (3pt)

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Transcript

00:01 We have an airplane that i'm going to draw from the side.

00:03 It kind of looks like this, and it's attached to a wire that has a length of 60 meters.

00:10 And the airplane has a mass of three quarters of a kilogram.

00:15 And there is a lift force that the plane is generating at a certain angle of 30 degrees relative to the vertical.

00:25 So that also means that this angle is going to be 30 degrees.

00:30 And we want to know a couple of things about this.

00:33 So first off, let's draw a free body diagram for the plane.

00:35 So the free body diagram, we have the weight of the plane going down this way.

00:39 We have the tension in the line going this way.

00:43 And the centripetal force goes this way because the plane is moving in a circle.

00:49 So those are all of our forces to consider.

00:53 And we want to know what's the radius of the circular path of the plane.

00:56 Well, the radius is going to be basically just this distance.

00:58 So it'll be l times the cosine of 30 degrees.

01:04 So r is l times the cosine of 30.

01:06 60 meters times the cosine of 30, which is the square root of 3 over 2.

01:14 And so this should come out to something like 51 .96 meters.

01:25 That's the radius of this little trajectory.

01:29 And then what's the magnitude of the size? centripetal acceleration.

01:32 So the centripetal acceleration is going to be mv squared over r, very simple.

01:39 And so we have three -fourths of a kilogram times the speed squared, which is 35 meters a second.

01:46 I've got neglected to mention that divided by this 51 .96 meters.

01:52 So this is our centripetal force.

01:56 I think, sorry, it asked for the centripetal acceleration, not the centripetal force.

02:00 So we just got to get rid of this m here...

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