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Question 1.

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Question 2 Picture.

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undo

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Question 1 & 2

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The example of banking and utilizing the frictional force is to do cornering, there are 2 way to utilize the frictional force, the first method is for soft compound tire, by lowering your speed and letting the tire to get a better grip at the leaning angle, you can then increase your speed once the tire have enough grip so you don't lose traction nor skid, the 2nd method is for slick tire’s as you dont need to lower your speed too much and lose velocity and it can allow us to still do banking even at high torque, the slick tire is very sticky to asphalt and having very high friction allowing us to do corner’s easily without losing traction

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The example of banking and utilizing the frictional force is to do cornering, there are 2 way to utilize the frictional force, the first method is for soft compound tire, by lowering your speed and letting the tire to get a better grip at the leaning angle, you can then increase your speed once the tire have enough grip so you don't lose traction nor skid, the 2nd method is for slick tire’s as you dont need to lower your speed too much and lose velocity and it can allow us to still do banking even at high torque, the slick tire is very sticky to asphalt and having very high friction allowing us to do corner’s easily without losing traction

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Equation: (mwr^2)

sorry ms I meant Merry-go-round**

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Fc = Ff

Fc = Fk (A frictional force that is moving is called kinetic friction)

=

Fc = mv^2/r

Fk= μk mg

mv^2/r = μk mg r

———       ———

m.             m

√v^2 = √μk g r

v = √μk g r

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Not only due to the angle. But whenever there is a maximum height reached then the speed is 0. Thus it is impossible for the speed to be 0 all the time. This being said, the speed in a vertical circular motion is not constant.

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Equation:
Fc = Fk

Fc = mv^2/r

Fk= μk mg

mv^2/r = μk mg r

———       ———

m.             m

√v^2 = √μk g r

v = √μk g r

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Fc = Fk
Fc = mv^2/r
Fk= μk mg
mv^2/r = μk mg r
———       ———
m.             m
√v^2 = √μk g r
v = √μk g r

(if you cannot hear the last part)
and then the final answer to get the max speed of the car is v equals to square root of Mu times g times r