A 7900- helicopter accelerates upward at 0.90 while lifting a 1100- frame at a construction site.
A) What is the lift force exerted by the air on the helicopter rotors?
B)What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?
C)What force does the cable exert on the helicopter
Your numbers require dimensions.
The forace exerted by the air
The problem does not state units, this assuming the weight is Kg and acceration is m/s2
g = 9.8
a = .9
from Netwon law
sum of force= ma
helicopter weight + frame weight X g + frame weight X a= force exerted by air
Force =(7900+1100) x 9.8 + (1100 x .9)
tension on the cabel
the forces acting on the cable is the frame
frame weight X g + frame weight X a= Tension in the cable
1100 x 9.8 + 1100 x .90=
why would the force of the air ONLY act on the frame? Isn't it also acting on the helicopter?
To answer these questions, we need to use Newton's laws of motion.
Let's start with part A:
A) What is the lift force exerted by the air on the helicopter rotors?
According to Newton's second law, the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the helicopter is accelerating upwards.
The net force can be determined by using the equation:
Net force = mass * acceleration
Given:
Mass of the helicopter = 7900 kg
Acceleration = 0.90 m/s^2
Net force = 7900 kg * 0.90 m/s^2
Net force = 7110 N
So, the lift force exerted by the air on the helicopter rotors is 7110 Newtons.
Moving on to part B:
B) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?
In this scenario, the helicopter is lifting a frame using a cable. The tension in the cable can be found by considering the forces acting on the frame.
There are two forces acting on the frame:
1. Weight force acting downward due to gravity
2. Tension force acting upward due to the cable
When a body is in equilibrium (static or dynamic), the sum of all the forces acting on it is zero.
In this case, the tension in the cable is equal to the weight force of the frame. So, the tension in the cable can be calculated as:
Tension in the cable = Weight of the frame
Given:
Mass of the frame = 1100 kg
Acceleration due to gravity = 9.8 m/s^2
Weight of the frame = mass * acceleration due to gravity
Weight of the frame = 1100 kg * 9.8 m/s^2
Weight of the frame = 10780 N
Therefore, the tension in the cable that connects the frame to the helicopter is 10780 Newtons.
Moving on to part C:
C) What force does the cable exert on the helicopter?
According to Newton's third law, for every action, there is an equal and opposite reaction. So, the force exerted by the cable on the helicopter is equal to the force exerted by the helicopter on the cable. In this case, it will be equal to the tension in the cable.
Therefore, the force the cable exerts on the helicopter is also 10780 Newtons.