The model airplane in figure below is flying at a speed of 21 m/s on a horizontal circle of radius 18 m. The mass of the plane is 0.82 kg. The person holding the guideline pulls it in until the radius becomes 11 m. The plane speeds up, and the tension in the guideline becomes four times greater. What is the net work done on the plane?

Question

The model airplane in figure below is flying at a speed of 21 m/s on a horizontal circle of radius 18 m. The mass of the plane is 0.82 kg. The person holding the guideline pulls it in until the radius becomes 11 m. The plane speeds up, and the tension in the guideline becomes four times greater. What is the net work done on the plane?

The answer will be in Joules.

Answer 1

m•v1²/R1=T1

m•v2²/R2=T2=4•T1
v2²=4•v1²•R2/R1
W=KE2-KE1 = m•v1²/2 - m•v2²/2 =
= m•v1²/2- m• 4•v1²•R2/2•R1 =
= m•v1² { 1- (2•R2/R1)}/2=
= 0.82•21²{1-(2•18/11)}/2 = - 411 J.

Answer 2

hmm this isnt the write answer, i wonder what went wrong?

Answer 3

To find the net work done on the plane, we need to calculate the change in kinetic energy of the plane.

The initial speed of the plane, vi = 21 m/s
The initial radius of the circle, ri = 18 m
The final radius of the circle, rf = 11 m

First, let's calculate the initial kinetic energy of the plane, Ki:
Ki = (1/2) * m * vi^2

Substituting the given values:
Ki = (1/2) * 0.82 kg * (21 m/s)^2

Next, let's calculate the final kinetic energy of the plane, Kf:
Kf = (1/2) * m * vf^2

To find vf, we can use the conservation of energy principle. The work done by tension is equal to the change in kinetic energy:

Work done by tension = ΔK
Tension * distance moved = Kf - Ki

Given that the tension becomes four times greater, the new tension can be expressed as:
New Tension = 4 * Initial Tension

Since the tension is directly proportional to the force applied by the person, we can write:
New Tension = 4 * Initial Tension = 4 * Tension

The work done by tension is given by:
Work done by tension = Tension * distance moved
= 4 * Initial Tension * (2 * π * ri - 2 * π * rf)
= 4 * Initial Tension * 2 * π * (ri - rf)

Now, since the work done by tension is equal to the change in kinetic energy, we have:
4 * Initial Tension * 2 * π * (ri - rf) = Kf - Ki

Now, we need to solve for Kf - Ki (the change in kinetic energy).

Kf - Ki = 4 * Initial Tension * 2 * π * (ri - rf)

Finally, the net work done on the plane is equal to the change in kinetic energy:
Net Work = Kf - Ki
= 4 * Initial Tension * 2 * π * (ri - rf)

You can now substitute the given values for initial tension (not provided), ri, and rf to determine the net work done on the plane in Joules.