On an aircraft carrier, a jet can be catapulted from 0 to 175 mi/h in 2.00 s. If the average force exerted by the catapult is 4.2 106 N what is the mass of the jet?
175 mi/h = 78.2 m/s
change in momentum = 78.2 * m
force = change in momentum / time
4.2*10^6 = 78.2 * m / 2
solve for m
V = 175mi/h * 1600m/mi * 1h/3600s = 77.8 m/s.
V = Vo + a*t.
77.8 = 0 + a*2,
a = 38.9 m/s^2.
Fap = M*a.
4.2*10^6 = M*38.9,
M = ?.
1.07 *10^3
To find the mass of the jet, we can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration. In this case, we have the force (4.2 × 10^6 N) and the acceleration (change in speed divided by the time, which is (175 mi/h - 0 mi/h) / (2 seconds)).
First, let's convert the speed from miles per hour to meters per second since we're using the metric system in physics. We know that 1 mile = 1609 meters and 1 hour = 3600 seconds, so we have:
Speed = (175 mi/h) × (1609 m/1 mi) / (3600 s/1 h)
Calculating this, we get:
Speed = 78.15 m/s
Now, we can calculate the acceleration using:
Acceleration = (Change in speed) / (Time)
Acceleration = (78.15 m/s - 0 m/s) / 2 s
Acceleration = 39.07 m/s^2
Next, we can rearrange Newton's second law to solve for the mass:
Force = Mass × Acceleration
Mass = Force / Acceleration
Substituting the values we have:
Mass = (4.2 × 10^6 N) / (39.07 m/s^2)
Calculating this, we get:
Mass = 107416.77 kg
Therefore, the mass of the jet is approximately 107,416.77 kg.