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A 1400 kgjet engine is fastened to the fuselage of a passenger jet by just three bolts (this is the usual practice). Assume that each bolt supports one-third of the load. (a) Calculate the force on each bolt as the plane waits in line for clearance to take off. (b) During flight, the plane encounters turbulence, which suddenly imparts an upward vertical acceleration of2.6m/s2to the plane. Calculate the force on each bolt now.

Short Answer

Expert verified

(a) Force on each bolt when plane waits in line for clearance to take off is4.6103N

(b) Force on each bolt when there is turbulence of air imparts upward acceleration is 5.8103N.

Step by step solution

01

Given information

1) m=1400 kg

2)a=2.6m/s2

02

Understanding the concept

Newton鈥檚 second law states that the net force on the body is equal to the product of mass of the body and the acceleration with which body is moving.

Apply Newton鈥檚 second law to find force on each bolt, when the plane is at rest and when it is in motion.

03

Formula used

Formulae:

  1. W=mg
  2. F=ma

Here,W is weight of the object,m I s mass of the object,g is gravitational acceleration,F is force anda is acceleration of the object.

04

(a) Calculate the force on each bolt when plane is at rest

Apply Newton鈥檚 second law, net force on plane is,

Fnet=3F-mg

Here 3F is the force on three bolts.

For rest, Fnet=0

0=3F-1400kg9.8m/s2F=1400kg9.8m/s23=4.6103N

Therefore, the force on each bolt is 4.6103N.

05

(b) Calculate the force on each bolt when plane is in motion

When the plane is in the motion, it will have some acceleration. Using the equation of motion, we can write,

ma=3F-mgF=ma+g3=1400kg2.6/s2+9.8m/s23=5.8103N

Therefore, the force on each bolt is 5.8103N.

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