PLEASE ANSWER ALL FOUR QUESTIONS WITH WORK SHOWN. A 100 kg pilot is executing a

Question

PLEASE ANSWER ALL FOUR QUESTIONS WITH WORK SHOWN.

A 100 kg pilot is executing a vertical circular loop of radius 1000 meters in his plane above the earth at a constant speed of 200 m/s. Assuming the acceleration due to earth's gravity is constant, the force by the seat on the pilot at the lowest point of the loop would be 5000n 4000n 3000n 1500n 100 n In terms of acceleration due to earth's gravity g, how many "g"s will be experienced by the pilot at the lowest point of the loop? lg 2g 3g 4g 5g A block of 1 kg mass is pulled from rest in the horizontal x-direction with a displacement dependent force F = 4x + 2. The change in kinetic energy in moving the block a distance of 2 meters would be The velocity of the block after traveling a distance of 2 meters would be 5.3 m/s 4.6 m/s 3.7 m/s 3.2 m/s 2.8 m/s

Explanation / Answer

19 )

At the lowest point forces are gravity and centrifugal force

--->F=Mg+Mv^2/R

F=1000+4000

=5000 N

20)

F=Ma

5000=100*a

--->g force=5 g=a

21) change in K.E is due to horizontal component only

F=(4x+2) cos(30)

Ma=M*dv/dt

--->M*(dv/dx)*(dx/dt)

but dx/dt=v

--->F=Mv*dv/dx

now integrating this equatioin in limits x=0 to x=2 gives

4(x^2+x)*cos(30)= 2*Change in K.E

--->Change in K.E= 10.39 J

velocity of block=sqrt(12sqrt(3)) with in limits 0 to 2

v=4.559 m/sec

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