Question

An aeroplane is flying at 100m/d, it dives along a vertical circle of radius 200m. Mass of pilot is 75 kg. What force is on pilot by seat of plane when it is at maximum and minimum height?

Answer 1

Answer on Question #47831 – Engineering – Other

1. An aeroplane is flying at $100\,\mathrm{m/s}$, it dives along a vertical circle of radius $200\,\mathrm{m}$. Mass of pilot is $75\,\mathrm{kg}$. What force is on pilot by seat of plane when it is at maximum and minimum height?

When the plane is at maximum height, the acceleration is directed downwards, so the weight of the pilot is $P = m(g - a)$. When the plane is at minimum height, the acceleration is directed upwards, so the weight of the pilot is $P = m(g + a)$.

The force acting upon the pilot equals to pilot’s weight, but the direction of it is opposite. Thus,

$$\boxed{F_1 = m\left(g - \frac{v^2}{r}\right)}, \quad \boxed{F_2 = m\left(g + \frac{v^2}{r}\right)}.$$

Let check the dimension: $\left[F_1\right] = \left[F_2\right] = kg \cdot \left(\frac{m}{s^2} + \frac{(m/s)^2}{m}\right) = \frac{kg \cdot m}{s^2} = N$.

Let evaluate the quantities: $F_1 = 75 \cdot \left(9.81 - \frac{100^2}{200}\right) = -3010(N)$,

$$F_2 = 75 \cdot \left(9.81 + \frac{100^2}{200}\right) = 4490(N).$$

Answer: $-3010N$, $4490N$.

https://www.AssignmentExpert.com