On an aircraft carrier, a jet can be catapulted from 0 to 155 mi/h in 2.00 s. If the average force exerted by the catapult is 5.53×106 N what is the mass of the jet?__________ kg
Why did the jet go to a psychologist?
Because it had a lot of weight on its mind! And speaking of weight, let's calculate it for you.
The average force exerted by the catapult is 5.53×10^6 N, and we can use Newton's second law (F = ma) to find the mass of the jet. We know the force (F) and we need to find the mass (m).
Rearranging the equation, we have m = F/a, where F is the force exerted by the catapult and a is the acceleration of the jet.
The acceleration of the jet is given by a = (change in velocity) / (time taken).
Given the change in velocity is from 0 to 155 mi/h = 69.384 m/s, and the time taken is 2.00 s, we can plug these values into the equation to calculate the acceleration.
a = 69.384 m/s / 2.00 s = 34.692 m/s²
Now, let's calculate the mass:
m = 5.53×10^6 N / 34.692 m/s²
Calculating this gives:
m ≈ 159,399 kg
So, the mass of the jet is approximately 159,399 kg. That's quite a heavy jet, but it's ready to take flight!
To find the mass of the jet, we can use Newton's second law of motion, which states that force (F) equals mass (m) multiplied by acceleration (a).
Given:
Initial velocity (u) = 0
Final velocity (v) = 155 mi/h (which needs to be converted to m/s)
Time (t) = 2.00 s
Force (F) = 5.53 × 10^6 N
First, let's convert the final velocity from mph to m/s:
1 mi/h = 0.44704 m/s
155 mi/h = 155 × 0.44704 m/s = 69.6032 m/s
Next, let's calculate the acceleration:
The formula for acceleration (a) is:
a = (v - u) / t
Substituting the given values:
a = (69.6032 m/s - 0) / 2.00 s
a = 69.6032 m/s / 2.00 s
a = 34.8016 m/s^2
Now we can use Newton's second law of motion to find the mass:
F = m × a
Substituting the values:
5.53 × 10^6 N = m × 34.8016 m/s^2
Rearranging the equation to solve for mass (m):
m = F / a
Substituting the given values:
m = 5.53 × 10^6 N / 34.8016 m/s^2
Calculating the mass:
m ≈ 158,793.55 kg
Therefore, the mass of the jet is approximately 158,793.55 kg.
To determine the mass of the jet, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the force exerted by the catapult is given as 5.53×10^6 N, and the acceleration of the jet is the change in velocity over time.
First, let's convert the velocity from miles per hour to meters per second. Since 1 mile is equal to 1609.34 meters and 1 hour is equal to 3600 seconds, we can calculate:
155 mi/h = (155 * 1609.34 m) / (1 h * 3600 s) = 69.1 m/s
Next, we can calculate the acceleration of the jet. Acceleration is defined as the change in velocity divided by the time taken:
acceleration = change in velocity / time taken
acceleration = 69.1 m/s / 2.00 s = 34.55 m/s^2
Now, we can rearrange Newton's second law to solve for the mass of the jet:
force = mass * acceleration
mass = force / acceleration
mass = 5.53×10^6 N / 34.55 m/s^2 ≈ 1.60 x 10^5 kg
Therefore, the mass of the jet is approximately 1.60 x 10^5 kg.
155 mi/h =69.3 m/s
v=at
a=v/t=69.3/2=34.65 m/s²
F=ma
m=F/a=5.53•10⁶/34.65=1.6•10⁵kg