Question

A parabolic bowl with. its bottom at origin has the shape y=xsquare/20 where x and y are in meter . The maximum height at which a snall mass m can be placed on the bowl without slipping is (coefficient of static friction =0.5).

Answer 1

Given:

Shape of the bowl at the bottom,

y = x^2/20

x,y are in meter.

Coefficient of static friction =0.5

Solution:

The frictional force will act in the direction tangentially to the bowl.

Friction, f = umg  

Now,

tan Θ = 2x/20

tan Θ = x/10

sin Θ = x/ √(x^2 + 100)

Therefore,

mgsin Θ  = f

mgsin Θ = umg

0.5 = x/√(x^2 + 100)

x^2 / (x^2 +  100) = 1/4

4x^2 = x^2 + 100

3x^2 = 100

x = 10/√(3) m.

The maximum height at which a snall mass m can be placed on the bowl without slipping is 10/√(3) m.

Answer 2

Answer:

Explanation:

Hope it will help you