1. When the helicopter is moving at a constant velocity, is there a net force acting on it?
No, there is no net force acting on the helicopter when it is moving at constant velocity. The force of gravity is matched by the lift of the helicopter, giving the helicopter a net force of 0.
2. The helicopter first moves up, and then you caused it to hover (or attempted to cause it to hover). Did there have to be a negative net force acting on the craft at some point for this to occur? Why?
Yes, there had to be a negative net force for this to happen. Although the acceleration could have been set to zero, because the helicopter required a positive acceleration to lift up, without a negative net force at some point, the helicopter will maintain a positive constant speed. After there is a negative net force, the helicopter's speed can be reduced to zero then its acceleration can become 0 as well.
Exercise 2: What is the mass of the helicopter?
(Force, Acceleration) Data point 1 (2250 N, 1.10) Data point 2 (25000 N , 12.25)
3. Does the acceleration change with the net force? What is the mathematical relationship of acceleration and net force?
Acceleration changes with net force directly. As Net force increases, acceleration will increase proportionally.
4. What is the mass of the helicopter? How did you determine it?
The mass of the helicopter is 2041 kg. This is the force divided by acceleration. I averaged together the two masses from the two data points.
Exercise 3: Net force and acceleration
5. What lift force was required to save the day?
32,002.88 N is required. This can be calculated by (9.80m/s2 + 5.88m/s2) * 2041kg.
Exercise 4: Air resistance
(Speed, Force) Data point 1 (7.94 m/s, 500 N) Data point 2 (15.89 m/s, 2000 N) Data point 3 (21.02 m/s, 3500 N) Data point 4 (25.13 m/s , 5000 N)
6. Look at your data. How does the force of air resistance vary with the speed of the helicopter? Does the force of air resistance increase as helicopter speed increases, decrease as helicopter speed increases, stay the same, or is there no relationship at all? Use your data to justify your answer.
The data is best fitted by a power regression model. The approximate equation is Force = 8 * speed^2.The force of air resistance therefore increases with the increase of the helicopter speed.The force of air resistance will grow faster that the speed.
7. Using the guidelines above, is the relationship between air resistance force and helicopter speed a linear, inverse, or squared relationship? Or is there no relationship at all? Justify your answer using your data.
There is a squared relationship between air resistance force and helicopter speed.The best fit equation is Force = 8 * speed^2.This can be determined by finding the best fit linear model for the data (ln(speed),ln(Force) and then solving for Force.The r value is greater for the linear equation (with the ln data) than for a normal linear equation (with the original data).
Exercise 5: Flying your helicopter
8. What horizontal thrust force is required for the helicopter to have zero horizontal velocity? To be moving at a constant horizontal velocity?
0N is the required horizontal thrust force for the helicopter to have zero horizaontal velocity becuase there is no acceleration at zero horizontal velocity.To be moving at a constant horizontal velocity, the required horizontal thrust force is also 0N.The reason for this is that if the acceleration is 0, then the force is 0, and the speed can be whatever, just as long as it is constant.
Exercise 6 (optional): Save the day!
9. What is the required lift force? Given this lift force, what are the net horizontal and vertical forces?
The required lift force is 25,505N. The net horizontal force is 4429N. The net vertical force is 25118N.