Francesca, who likes physics experiments, dangles her watch from a thin piece of
ID: 1419887 • Letter: F
Question
Francesca, who likes physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK airport. She notices that the string makes an angle of 12 degrees with respect to the vertical as the aircraft accelerates for takeoff, which takes about 48 s. The mass of the aircraft was 220,000 kg .A- Estimate takeoff distance B- find the thrust of the two aircraft engines at takeoff. How does it compare to the aircrafts weight Francesca, who likes physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK airport. She notices that the string makes an angle of 12 degrees with respect to the vertical as the aircraft accelerates for takeoff, which takes about 48 s. The mass of the aircraft was 220,000 kg .
A- Estimate takeoff distance B- find the thrust of the two aircraft engines at takeoff. How does it compare to the aircrafts weight
A- Estimate takeoff distance B- find the thrust of the two aircraft engines at takeoff. How does it compare to the aircrafts weight
Explanation / Answer
theta=12 degrees ; time =48s
First find acceleration
x/9.8 = tan 12, x = horizontal acceleration, 9.8 is gravity
x = 0.0216 m/s^2
Vf = Vo + at
Vf = 0 + 0.0216 * 48
Vf = 1.041 m/s
Let T = tension in the string
t = angle theta
In the x direction
a{x} = Tsin(t)=Tsin12=.2079T
In the y-direction
a{y} = 0 because the aircraft is only accelerating in the x-direction during its takeoff roll
so Tcos(t) - mg = 0,
or Tcos(t) = mg
=>Tcos12=220,000x9.8
=>T=2204166.322
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