Question

Derive the maximum speed for the motion of the car moving in circular motion on a level road and
banked road


pls help​

Answer 1

Answer:

Hello

Explanation:

components Ncosθ vertically up and

f

s

sinθ vertically down, Nsinθ and

f

s

cosθ horizontally towards the centre of the circular path.

If v

max

is the maximum safe speed without skidding.

r

mv

max

2

=Nsinθ+f

s

cosθ

=Nsinθ+μ

s

Ncosθ

r

mv

max

2

=N(sinθ+μ

s

cosθ)....(1)

and

Ncosθ=mg+f

s

sinθ

=mg+μ

s

Nsinθ

∴mg=N(cosθ−μ

s

sinθ)...(2)

Dividing eq. (1) by eq. (2),

r.mg

mv

max

2

=

N(cosθ−μ

s

sinθ)

N(sinθ+μ

s

cosθ)

∴

rg

v

max

2

=

cosθ−μ

s

sinθ

sinθ+μ

s

cosθ

=

1−μ

s

tanθ

tanθ+μ

s

∴v

max

=

1−μ

s

tanθ

rg(tanθ+μ

s

)

...,.(3)