The model airplane is being spun at a speed of 20 m/s on a horizontal circle of radius 17 m. The mass of the plane is 0.86 kg. The person holding the guideline pulls it in until the radius becomes 13 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 is being spun at a speed of 20 m/s on a horizontal circle of radius 17 m. The mass of the plane is 0.86 kg. The person holding the guideline pulls it in until the radius becomes 13 m. The plane speeds up, and the tension in the guideline becomes four times greater. What is the net work done on the plane?

Answer 1

Well, conservation of momentum applies

I w1=Iw2

I =mr^2
w1=v/r=20/17 rad/sec
m(17)^2*20/17=m(13)^2 V/13

vfinal=20*17/13 m/s

now, figure change in Kinetic Energy
KEf-KEi=work
m(20^2)(4/13)=work

Answer 2

Thank you for helping me!

Answer 3

To find the net work done on the plane, we need to calculate the change in kinetic energy. The work done on an object is equal to the change in kinetic energy.

First, let's calculate the initial kinetic energy of the plane. The formula for kinetic energy is 1/2 * mass * velocity^2.

Initial kinetic energy = 1/2 * mass * (initial velocity)^2
= 1/2 * 0.86 kg * (20 m/s)^2
= 172 J

Next, let's calculate the final kinetic energy of the plane. Since the plane speeds up when the radius becomes 13 m, we need to find the new velocity.

To find the new velocity, we can use the concept of conservation of angular momentum. The formula to find the angular momentum of a rotating object is given by L = mvr, where L is the angular momentum, m is the mass, v is the velocity, and r is the radius.

According to conservation of angular momentum, initially, the angular momentum of the plane is the same as the final angular momentum.

Initial angular momentum = Final angular momentum

m * (initial velocity) * (initial radius) = m * (final velocity) * (final radius)

0.86 kg * 20 m/s * 17 m = 0.86 kg * (final velocity) * 13 m

Simplifying the equation, we can find the final velocity.

final velocity = (0.86 kg * 17 m * 20 m/s) / (0.86 kg * 13 m)
= 26.15 m/s

Now that we have the final velocity, we can calculate the final kinetic energy.

Final kinetic energy = 1/2 * mass * (final velocity)^2
= 1/2 * 0.86 kg * (26.15 m/s)^2
= 286.59 J

Finally, we can calculate the net work done on the plane.

Net work done = Final kinetic energy - Initial kinetic energy
= 286.59 J - 172 J
= 114.59 J

Therefore, the net work done on the plane is 114.59 J.