Question

derive an expression for the minimum speed of the vehicle which derive in horizontal circle (well of death )
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Answer 1

Answer:

the frictional force must be greater than or equal to mg for body to move in circular motion and not fall

so the velocity must be greater than or equal to root over gr/u

Answer 2

The minimum force of the vehicle is rg/μ.

Given;

Horizontal circle.

To find:

Minimum speed of the vehicle.

Solution:

If we throw a marble on a ground, and it start to move with a velocity, and it should not be acting in the direction of motion, as we know according to the first law of Newton, it should keep moving, but the marble stops after moving for a certain time, from this example we can see a force  acting on it and the force is called as friction.

Force that makes a body follow a  particular curved path is called as centripetal force.

Friction of its weight and centripetal force are thhe only forces acting on the vehicle when it is rotating.

The weight and frictional force must be balanced so that it won't fall.

Friction =μ× Normal force.

The normal force which is required is given by centripetal force.

Normal force= $\frac{mv^{2} }{r}$  

Here we have,

Mass of the motorcycle= m,

Velocity= v ,

Radius of the death well=r

Therefore,

f=μ$\frac{mv^{2} }{r}$

Friction should be equal to its weight or greater,

μ$\frac{mv^{2} }{r}$ ≥mg

$v^{2}$ ≥rg/μ

∴v≥ _/(rg/μ)

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Hence the minimum force of the vehicle is rg/μ.

#SPJ6

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