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In this lesson, we will learn how to use the properties of the circular motion of objects moving in banked tracks to solve problems.

Q1:

A turn on a racing track follows a horizontal circular arc of radius 60 m. The track at this turn is banked at an angle of 2 0 ∘ to help motorcycles go round it at speed without slipping. Given that the maximum speed one particular motorcyclist can go around it without slipping is 89 km/h, find the coefficient of friction between her motorcycle’s tyres and the track. Take 𝑔 = 9 . 8 / m s 2 and give your answer correct to two decimal places.

Q2:

A particle moves along a horizontal circular path of radius 3.8 m at a constant speed of 3.8 m/s. What is the acceleration of the particle?

Q3:

A plane weighing 78 metric tons and flying at 749 km/h turned in a clockwise direction from due east to due south while banked at an angle 𝛼 to the horizontal, moving in a horizontal circular arc. If it took the plane 41 seconds to change its course, determine the magnitude of the lift force perpendicular to its wings. Give your answer correct to one decimal place. Take 𝑔 = 9 . 8 / m s .

Q4:

A turn on a racing track follows a horizontal circular arc of radius 148 m. The track is banked at this turn to help cars go round it at speed without slipping. The maximum speed that one of the racing cars can go around this turn without slipping is 156 km/h. Given that the coefficient of friction between this car’s tyres and the track is 0.23 and taking 𝑔 = 9 . 8 / m s 2 , find the angle to the horizontal at which the track is banked. Give your answer correct to one decimal place.

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