A 4600 kg helicopter accelerated upward at 5 m/s^2. What lift force is exerted by the air on the propellers?
--Would the downward force of gravity play a part in the solution?
The lift force on the propeller blades (F) is what keeps the helicopeter aloft and provides vertical acceleration.
F - Mg = Ma
Yes, the downward force of gravity does play a part in determining the lift force exerted by the air on the propellers of the helicopter. To find the lift force, we need to consider the upward acceleration of the helicopter and the force of gravity acting on it.
Let's break down the problem step by step:
Step 1: Calculate the force of gravity
The force of gravity, also known as the weight (W), is calculated using the formula:
W = mass x acceleration due to gravity
We can calculate the weight using the mass of the helicopter and the acceleration due to gravity (which is approximately 9.8 m/s^2):
mass = 4600 kg
acceleration due to gravity = 9.8 m/s^2
W = 4600 kg x 9.8 m/s^2
W = 45,080 N
So, the force of gravity acting on the helicopter is 45,080 Newtons (downward).
Step 2: Determine the net force
Since the helicopter is accelerating upward, we need to account for the net force acting on it. Net force is calculated using Newton's second law of motion:
Net force = mass x acceleration
In this case, the upward acceleration of the helicopter is given as 5 m/s^2, and the mass of the helicopter is 4600 kg.
Net force = 4600 kg x 5 m/s^2
Net force = 23,000 N (upward)
Step 3: Find the lift force
The lift force (L) is the force exerted by the air on the propellers of the helicopter. It is equal in magnitude but opposite in direction to the net force. So, the lift force can be calculated as:
L = Net force = 23,000 N (upward)
Therefore, the lift force exerted by the air on the propellers of the helicopter is 23,000 Newtons (upward).