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.

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)

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?

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)

Fc = m*v^2/r

The source of this force has to be the car's tires -- friction with the surface of the road. Friction is a force, Fc. The value of the maximum force the tires friction can provide is given by

Ff = mu*m*g

As the car tries to go faster through the curve and finally gets to the maximum, the value of Fc will be equal to the value of Ff. So

Fc = Ff

or

m*v^2/r = mu*m*g

Notice you don't need to know the mass. m cancels out. So

v^2/r = mu*g

Plug in the radius, the coefficient of friction (that's mu), the acceleration due to gravity and solve for v^2. Then take the sqrt.

2*pi*r = 2*pi*2.25 m = 14.14 m

So 14.14 m of rotation is equivalent to 360 degrees of rotation. So the fraction

14.14 m / 360 degrees would have a value of 1. Because if thing A = thing B and you divide thing A by thing B, the result is exactly 1.

Therefore:

A 3 m rotation is

3 m * (360 degrees/14.14 m) = ??? degrees

You can do that last bit.

Solve for r

So 30 cm = 0.30 m = 2*pi*r = pi*d

Solve for d.

1 .

r = 24 m

Âµ = 0.15

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

m * ( v Â² / r ) / m * g = 0.15

The m's cancel, leaving : ( v Â² / 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 Â°

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