Question

briefly explain how is vehicle able to go around a level curved track determine the maximum speed with which the vehicle can negotiate this curved track safetly

Answer 1

To go around a curve, the car needs to have a centripetal force applied, and friction with the road supplies that. We will then use the centripetal acceleration below.
Constants:

g=10 m/s2g=10 m/s2

Givens:

r=30 mr=30 m

μ=0.4μ=0.4

Unknowns:

v=?v=?

Other values to be used:

mm

It is useful to draw a force diagram on the car, which will have three forces:

FgFg down

FnormalFnormal up

FfrictionFfriction to the left or right.

The relevant relationships are

[1] m a⃗ =∑F⃗ m a→=∑F→

[2] Ffriction=μ FnormalFfriction=μ Fnormal

[3] Fgravity=m gFgravity=m g

[4] acentripetal=v2racentripetal=v2r

Eq [1] in the vertical direction gives

m(0)=Fnormal−Fgravity