A 12000 kg airplane launched by a catapult from an aircraft carrier is accelerated from 0 to 200 km/h in 3 s. (a) How many times the acceleration due to gravity is the airplane's acceleration? (b) What is the average force the catapult exerts on the airplane?
v=200 km/h =200000/3600=55.56 m/s,
a=(v-v₀)/t=(55.56-0 )/3=18.52 m/s²,
a/g= 18.52/9.8= 1.89,
F=ma=12000•18.52=2.22•10⁵ N
how did u get the 9.8?
(a) To find the airplane's acceleration, we first need to convert the initial and final velocities to meters per second.
Initial velocity = 0 km/h
Final velocity = 200 km/h
To convert km/h to m/s, we need to multiply by a conversion factor of 1000/3600:
Initial velocity = 0 km/h * (1000 m/3600 s) = 0 m/s
Final velocity = 200 km/h * (1000 m/3600 s) = 55.56 m/s
Next, we can use the formula for acceleration:
Acceleration = (Final velocity - Initial velocity) / Time
Acceleration = (55.56 m/s - 0 m/s) / 3 s = 18.52 m/s²
To find how many times the airplane's acceleration is the acceleration due to gravity, we can divide the two values:
Airplane's acceleration / Acceleration due to gravity
Acceleration due to gravity is approximately 9.8 m/s², so:
Airplane's acceleration / Acceleration due to gravity = 18.52 m/s² / 9.8 m/s² = 1.89
Therefore, the airplane's acceleration is approximately 1.89 times the acceleration due to gravity.
(b) To find the average force the catapult exerts on the airplane, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration:
Force = Mass * Acceleration
Given:
Mass = 12000 kg
Acceleration = 18.52 m/s²
Force = 12000 kg * 18.52 m/s² = 222240 N
Therefore, the average force the catapult exerts on the airplane is 222240 Newtons.
To solve these problems, we need to make use of Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
(a) How many times the acceleration due to gravity is the airplane's acceleration?
The acceleration due to gravity is approximately 9.8 m/s^2. We need to convert the velocity from km/h to m/s.
1 km/h = 1000 m/3600 s = 10/36 m/s
So, the final velocity of the airplane is:
v = (200 km/h) * (10/36 m/s) = 55.56 m/s
Now, we can calculate the acceleration of the airplane using the formula:
a = (v - u) / t
where:
a = acceleration
v = final velocity
u = initial velocity (0 m/s, because it starts from rest)
t = time taken
Substituting the values:
a = (55.56 m/s - 0 m/s) / 3 s ≈ 18.52 m/s^2
To find how many times the airplane's acceleration is compared to the acceleration due to gravity, we divide the airplane's acceleration by the acceleration due to gravity:
Number of times = a / (acceleration due to gravity)
Number of times = 18.52 m/s^2 / 9.8 m/s^2 ≈ 1.89 times
Therefore, the airplane's acceleration is approximately 1.89 times the acceleration due to gravity.
(b) What is the average force the catapult exerts on the airplane?
We can use Newton's second law of motion to find the average force exerted by the catapult. Rearranging the formula:
Force = mass * acceleration
We have the mass of the airplane given as 12000 kg and the acceleration calculated as 18.52 m/s^2.
Force = (12000 kg) * (18.52 m/s^2) = 222240 N
Therefore, the average force exerted by the catapult on the airplane is 222240 Newtons.