Dynamics question please help i am stuck...!
A model helicopter of mass 5.0 kg rises with constant acceleration from rest to a height of 60 m in 10 seconds. Find the thrust exerted by the rotor blades during the ascent
Thrust required to keep the helicopter stationary
= weight of helicopter
= mg
To find the vertical (upwards) acceleration, we use the formula:
S=ut+(1/2)at²
where
S = distance = 60m
u = initial velocity = 0
t = time = 10 s
a=2(S-ut)/t²
=2(60-0)/10²
=1.2 m s-2
Total thrust
= 5 kg ( 9.8 + 1.2 ) m s-2
= 55 N
To find the thrust exerted by the rotor blades during the ascent of the helicopter, we can use the equation for acceleration:
acceleration = change in velocity / time
First, let's find the change in velocity. Since the helicopter starts from rest, the initial velocity is 0 m/s. The final velocity can be found using the equation:
final velocity = initial velocity + (acceleration * time)
We can rearrange the equation to solve for acceleration:
acceleration = (final velocity - initial velocity) / time
Given that the final velocity is unknown, we can determine it using the equation for displacement:
displacement = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the displacement is known as 60 m, we can rearrange the equation to solve for the final velocity:
60 = (0 * 10) + (0.5 * acceleration * 10^2)
Now, substitute the value of the acceleration into the equation and solve for the final velocity:
60 = 0.5 * acceleration * 100
Dividing both sides by 50 will give:
1.2 = acceleration
Now, using the equation for acceleration, we can determine the thrust:
thrust = mass * acceleration
Substituting the values:
thrust = 5.0 kg * 1.2 m/s^2
Calculating, we find:
thrust = 6.0 N
Therefore, the thrust exerted by the rotor blades during the ascent of the helicopter is 6.0 N.
To find the thrust exerted by the rotor blades during the ascent of the model helicopter, we can use Newton's second law of motion.
Newton's second law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the object is the model helicopter and the force is the thrust exerted by the rotor blades.
Given:
Mass of the helicopter (m) = 5.0 kg
Height (h) = 60 m
Time taken (t) = 10 seconds
First, let's find the acceleration of the helicopter. We can use the equation of motion:
h = (1/2) * a * t^2
Substituting the given values:
60 = (1/2) * a * (10)^2
Rearranging the equation to solve for acceleration (a):
a = (2 * h) / t^2
a = (2 * 60) / (10)^2
a = 12 m/s^2
Now that we have the acceleration, we can find the thrust using Newton's second law:
Force (F) = mass (m) * acceleration (a)
F = 5.0 kg * 12 m/s^2
F = 60 N
Therefore, the thrust exerted by the rotor blades during the ascent of the model helicopter is 60 Newtons.