Question

a 47.0 kg stunt pilot who has been diving her airplane vertically pulls out of the dive by changing her course to a circle in a vertical plane.if the plane's speed at the lowest point of the circle is 96.0 m/s , what is the minimum radius of the circle so that the acceleration at this point will not exceed 4.00 g ?what is the apparent weight of the pilot at the lowest point of the pullout?

Answer 1

The minimum radius of the circle is approximately 236m and the apparent weight of the pilot at the lowest point of the pullout is 1843.6N.

Step-by-step explanation:

To calculate the minimum radius of the circle, we need to first find the acceleration at the lowest point of the pullout. The centripetal acceleration is given by a = v^2 / r, where v is the speed and r is the radius. Since the acceleration should not exceed 4.00 g, we have a <= 4.00 * 9.8 m/s^2. Rearranging the equation, we get r >= v^2 / (4.00 * 9.8).

Substituting the given values, r >= (96.0)^2 / (4.00 * 9.8) = 235.96 m. Therefore, the minimum radius of the circle is approximately 236 m.

The apparent weight of the pilot at the lowest point of the pullout can be calculated using the equation F_net = m * (g + a), where F_net is the net force, m is the mass, g is the acceleration due to gravity, and a is the centripetal acceleration. Since the pilot experiences an upward force due to the normal force, we can write F_net = m * (g + a) - m * g. Rearranging the equation, we get F_net = m * a. Substituting the given values, F_net = (47.0 kg) * (4.00 * 9.8 m/s^2) = 1843.6 N.

Answer 2

The minimum radius of the circle is determined as 313.5 m.

The apparent weight of the pilot is 921.1 N.

How to calculate the minimum radius of the circle?

The minimum radius of the circle is calculated by applying the following formula as shown below;

The net force at the lowest point of a circle is;

T - mg = mv²/r

r = mv² / (T - mg)

r = mv²/ (ma - mg)

where;

• m is the mass of the pilot
• v is the speed
• g is acceleration due to gravity
• a is acceleration of the pilot

r = mv²/ (ma - mg)

r = v²/ (a - g)

r = v² /(4g - g)

r = v² / 3g

r = (96² ) / ( 3 x 9.8)

r = 313.5 m

The apparent weight of the pilot is calculated as;

W' = mv²/r - W

W' = (47 x 96²)/313.5 - (47 x 9.8)

W' = 921.1 N