a)
b) 803.4 N
Explanation:
a)
At the point C (top position of the loop), the pilot feel weightless, so the normal reaction exerted by the seat is zero:
N = 0
Therefore, the equation of the forces at position C is:
where the term on the left is the weight of the pilot and the term on the right is the centripetal force, and where:
is the acceleration due to gravity
is the velocity of the jet at the top
is the radius of the loop
Solving for v,
So, this is the velocity of the jet at position C.
The velocity at position A (bottom) is
The distance covered by the jet is the length of a semi-circumference of radius r, so
Since the deceleration of the plane is constant, we can find it by using the following suvat equation:
b)
The force exerted on the pilot by the seat is equal to the normal force.
At point B (half of the loop), we have:
- The normal force exerted by the seat, N, acting towards the center of the loop
- There are no other forces acting towards the center of the loop, so N must be equal to the centripetal force:
(1)
where is the velocity at position B.
To find the velocity at position B, we notice that the distance covered by the jet between position A and position B is a quarter of a circle:
Since we know the deceleration, we can use the suvat equation to find the velocity at point B:
Therefore, we can now use eq.(1) to find the normal force exerted by the seat on the pilot at point B: