A 33 tonnes jet airline has 4 engines,each producing a nearly constant thrust of 165kN during the takeoff roll.Determine the length of the runway required if the takeoff speed is 320km/h.Neglect air and rolling resistance.
320,000 m/h /3600s/h = 88.9 m/s
v = a t
d = (1/2) a t^2
so
d= (1/2) v^2/a
d = (1/2) (88.9)^2/a
but a = 4*165,000 N /33,000 kg
= 20.6 m/s^2 (2 g, good grief)
so d = (1/2)(88.9)^2/20.6
= 191.6 meters
so there is no need to consider about the weight when finding the force? since F=ma, then i use 165000x4=33000xa to find acceleration rather than 165000x4-33000=33000xa ?
That is correct
and if you were to use the weight for example to calculate a friction force you would do weight = mg, not just m
Well, looks like we have a flying clown car here! Let's calculate the runway length required for this jumbo jet.
First, we need to convert the takeoff speed from kilometers per hour to meters per second. Since there are 3.6 seconds in an hour, we divide by 3.6 to get the equivalent in meters per second:
320 km/h ÷ 3.6 = 88.9 m/s
Now let's calculate the total thrust produced by all four engines:
4 engines x 165 kN = 660 kN
Next, we need to convert the thrust from kilonewtons to newtons, since the mass is given in tonnes (1 tonne = 1000 kg):
660 kN x 1000 = 660,000 N
Now we can use Newton's second law of motion to find the acceleration:
Force = Mass x Acceleration
660,000 N = 33,000 kg x Acceleration
Acceleration = 660,000 N ÷ 33,000 kg
Acceleration = 20 m/s^2
Now let's use the kinematic equation to find the required runway length:
v^2 = u^2 + 2as
where:
v = final velocity (takeoff speed) = 88.9 m/s
u = initial velocity (0 m/s, as the plane starts from rest)
a = acceleration = 20 m/s^2
s = runway length (what we want to find)
Rearranging the equation to solve for s, we get:
s = (v^2 - u^2) ÷ (2a)
s = (88.9^2 - 0^2) ÷ (2 x 20)
s = 790.41 m
So, the length of the runway required for this jumbo jet to take off is approximately 790.41 meters. Just make sure to paint some clown faces on the runway to give the passengers a smile as they take off!
To determine the length of the runway required for takeoff, we need to consider the forces acting on the aircraft during the takeoff roll. The most significant force is the thrust produced by the engines, which counteracts the aircraft's weight. We can use Newton's second law of motion to calculate the acceleration of the aircraft.
First, let's convert the takeoff speed from km/h to m/s:
Speed (m/s) = Speed (km/h) * 1000 / 3600
= 320 * 1000 / 3600
= 88.9 m/s (approximately)
Next, we need to calculate the total thrust produced by all four engines:
Total Thrust = Thrust per engine * Number of engines
= 165 kN * 4
= 660 kN
Since there is no air resistance and rolling resistance, the only force opposing the thrust is the weight of the aircraft. The weight of the aircraft can be calculated using the formula:
Weight = Mass * Gravity
Given that the mass of the aircraft is 33 tonnes, which is equivalent to 33,000 kg, and the acceleration due to gravity is approximately 9.8 m/s²:
Weight = 33,000 kg * 9.8 m/s²
= 323,400 N
Now we can calculate the acceleration of the aircraft using Newton's second law of motion:
Net Force = Total Thrust - Weight
Acceleration = Net Force / Mass
Acceleration = (660,000 N - 323,400 N) / 33,000 kg
= 336,600 N / 33,000 kg
= 10.2 m/s² (approximately)
Finally, we can calculate the length of the runway required using the kinematic equation:
Distance = (Speed² - Initial Speed²) / (2 * Acceleration)
Given that the initial speed is 0 m/s (since the aircraft starts from rest):
Distance = (88.9 m/s)² / (2 * 10.2 m/s²)
= 7887 m (approximately)
Therefore, the length of the runway required for takeoff is approximately 7887 meters.