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Problems on friction & banking angle

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1. Radio engineers are erecting a communications tower that is 16.0 m high. During the installation they stabilize the tower with 32.0 m long cables running from the top of the tower to the ground. The anchors consist of concrete blocks to which the cables can be secured. Each block weighs 1590 N. If the coefficient of static friction between a block and the ground is 0.800, what is the maximum tension that can exist in a cable before that cable's anchor is in danger of moving?

hint: you don't know the friction force at this point, so that doesn't necessarily help you immediately. You must write balance of forces equations in both the x and y directions. You have the x equation already. For the y equation, remember that there are three contributions: the weight of the block, the normal force on the block, and the vertical component of the tension on the cable. You will have to combine the x and y equations algebraically to find the result, also using the condition that friction = mu*(normal force) when the block is about to slide.

2. An airplane traveling at 529 km/hr needs to reverse its course. The pilot decides to accomplish this by banking the wings at an angle of theta = 41.0 degree.
a) Find the time needed to reverse course.
b) How heavy would a 56 kg passenger feel during the turn? In other words, what would be the magnitude of the total force exerted on the passenger by the airplane seat?

Hint: This is a banked turn problem. The force responsible for the turning (centripetal force) comes entirely from the horizontal component of the lift force. Note that the pilot will fly through half a circle while making the turn. You'll have to figure out the turning radius first, then the time to complete half a circle (not a whole circle!).
For part b) Your weight is what a scale would read if you were standing on it during the turn. This is equal to the normal force of the plane holding you "up", in the direction of the lift force on the banked plane.

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Solution Summary

These two problems on friction and banking angle of airplane have been solved step by step duly illustrated with figs.

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Physics 7th edition by Cutnell and Johnson: Uniform Circular Motion and Gravitation

Conceptual Questions:

1. An object is thrown upward at an angle above the ground, eventually return to earth. (a) Is there any place along the trajectory where the velocity and acceleration are perpendicular? If so, where? (b) Is there any place where the velocity and acceleration are parallel? If so, where? In each case, explain.

2. The speedometer of your car shows that you are traveling at a constant speed of 35 m/s. It is possible that your car is accelerating? If so, explain how could this happen?

3. The equations of kinematics (not included) describe the motion of an object that has a constant acceleration. These equations cannot applied to uniform circular motion. Why not?

4. It is possible for an object to have acceleration when the velocity of the object is constant? When the speed of the object is constant? When the speed of the object is constant? In each case, give your reasoning?

5. What is a chance of a light car safely rounding an unbanked curve on icy road as compared to that of heavy car: worse, the same, better? Assume that both cars have the same speed and equipped with identical tires. Account your answer.

6. A penny is placed on a rotating turntable. Where on the turntable does the penny require the largest centripetal force to remain in place? Give your reasoning.

Problems:

(Uniform Circular Motion & Centripetal Acceleration)

7. How long does it take a plane, traveling at a constant speed of 110 m/s, to fly around once around a circle whose radius is 2850 m?

8. A car travels at a constant speed around a circular track whose radius is 2.6 km. The car goes once around the track in 360 s. What is the magnitude of the centripetal acceleration of the car?

(Centripetal Force)

9. In a skating stunt known as "crack-the-whip," a number of skaters holds hands and form a straight line. They try to skate so that the line rotates about the skater at one end, who acts as a pivot. He is skating at a speed of 6.80 m/s. Determine the magnitude of the centripetal force that acts on him.

10. A child is twirling a 0.0120-kg ball on a string in a horizontal circle whose radius is 0.100 m. The ball travels once around the circle in 0.500 s. (a) Determine the centripetal force acting on the ball. (b) If the speed is doubled, does the centripetal force double? If not, by what factor does the centripetal force increase?

11. Two banked curves have the same radius. Curve A is banked at an angle of 13o, and banked B is curved at an angle of 19o. A car can travel around curve A without relying on friction at a speed of 18 m/s. At what speed these car travels around curve B without relying on friction?

(Satellites in Circular Orbits, Apparent weightlessness and Artificial Gravity)

12. A satellite is placed in orbit 6.00 x105 m above the surface of Jupiter. Jupiter has a mass of 1.90 x 1027 kg and a radius of 7.14 x 107. Find the orbital speed of the satellite.

13. A satellite is in a circular orbit about the earth (ME = 5.98 x 1024). The period of the satellite is 1.20 x 104 s. What is the speed at which the satellite travels?

14. The earth orbits around the sun once per year at the distance of 1.50 x 1011m. Venus orbits the sun at a distance of 1.08 x 1011 m. these distances are between the centers of the planets and the sun. How long (in earth days) does it take for Venus to make one orbit around the sun?

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