33. An airplane pilot is going to demonstrate flying in a tight vertical circle.

Question

33. An airplane pilot is going to demonstrate flying in a tight vertical circle. To ensure that she doesn't black ou at the bottom of the circle, the acceleration must not exceed 4.0g. If the speed of the plane is 50 m/s at the bot tom of the circle, what is the minimum radius of the cir- cle so that the 4.0g limit is not exceeded? 34. you about your a ball attached to the end of a string. The ball moves at a con- stant speed in a horizontal circle. (a) Can the string be exactly horizontal? Why or why not? (b) If the mass of the ball is 0.250 kg, the radius of the circle is 1.50 m, and it takes 1.20 s for the ball to make one revolution, what is the ball's tangential speed? (c) What centripetal force are you imparting to the ball via the string? 35. In Exercise 34, if you supplied a tension force of 12.5 N to the string, what angle would the string make relative to the horizontal? 36. A car with a constant speed of 83.0 km/h enters a cir- cular flat curve with a radius of curvature of 0.400 km. If the friction between the road and the car's tires can sup- ply a centripetal acceleration of 1.25 m/s does the car negotiate the curve safely? Justify your answer.

Explanation / Answer

35)

Weight of ball: m*g

Only the vertical component supports the ball's weight. The horizontal component rather provides the net force causing the acceleration inward. We aren't interested in the kinematics.

Equate the vertical component, T*sin(theta), to the weight:
T*sin(theta) = m*g = 0.250kg*9.81

m = 0.250kg

g =9.81

Solve for theta:
sin(theta) = m*g/T

theta = arcsin(m*g/T)

Result:
theta = 11.31 degrees35)

36)

speed of 83.0 km/h

radius of curvature of 0.400 km

centripetal acceleration of 1.25 m/s^2

a = v^2 / r
where a is the centripetal acceleration and v = speed and r is radius

v = 83*10^3 / 3600 = 415/18 m/s

So a = 415^2 / (18^2*0.4*10^3) = 1.33m/s^2

This is obviously more than 1.25m/s^2 so no it will not negotiate the curve safely

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