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Help me with these physics questions please?

Please help me answer these questions. I don't know what topic(s) they are from, though.

Please explain how to do it if you can and please state which formulas I should use. I really have no idea what topic this is but I think its related with Angular Displacement and Tangential Velocity because that's what we've been studying since last week.

  1. An object has to go around a horizontal curve of radius 24m curve. If the coefficient of friction between the object and the curved surface is 0.15, what is the maximum speed at which the object can go around the curve? (Help. I don't really understand this question)

  2. Bert rides on a merry-go-round at a distance of 2.25m from the center. If Bert moves through an arc length of 3m, through what-a triangle and theta is written here, lol xD is it angle theta?- does he moved?

  3. A compass draws a circle of a piece of paper 30cm in circumference. What was the distance of the needle to the pen of the compass when the circle was drawn? What is the diameter of the circle drawn?

Thank you, and pleaseeee explain if you can.

Answers (2)

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1 .

r = 24 m

µ = 0.15

The force required to break grip / the force down due to gravity = 0.15

m * ( v ² / r ) / m * g = 0.15

The m's cancel, leaving : ( v ² / r ) / g = 0.15

Transpose to feature v : v = square root ( 0.15 * g * r )

v = 5.94 m/s

2 .

The circumference of the circle = 2 * pi * 2.25 = 14.137 meters

The angle turned through = ( 3 / 14.137 ) * 360 = 76.39 °

3 .

Use the classic equation : circumference = 2 * pi * radius

Transpose to feature radius :

radius = circumference / ( 2 * pi )

radius = 4.77465 cm

diameter is 2 * radius = 9.54930 cm