Conservation of Energy question

[zheng89120]

Homework Statement

A hemispherical Bowl of mass M rests on a table. The inside surface of the bown is frictionless, while the coefficient of friction between the bottom of the bowl and the table is u = 1. A particle of mass m is released from rest at the top of the bowl and slides down into it, as shown in Fig. 5.38. What is the largest value of m/M for which the bowl never slides on the table? Hint: the angle you're concerned with is not 45.

Homework Equations

Energy conservation, maybe Newton's equations

The Attempt at a Solution

some form of sigma E = sigma E, not sure

 

[Lok]

Please send Fig 5.38
And what angle is that in the hint, maybe the Fig will help.

Considering that you have Friction and falling bodies start by writing the relevant equations of these and look for how many unknowns you have.

 

[zheng89120]

Figure 5.38 is on:

http://books.google.ca/books?id=Ni6...erical Bowl of mass M rests on a table&f=true

 

[hikaru1221]

First, only consider the situation where the bowl stays at rest. In this case, m performs circular motion. Find the normal force N_m on m in terms of its speed v and its angle position theta. The speed v can be found using the law of energy conservation.

Next, draw a force diagram for the bowl M. Find the normal force N_M acting on it and the horizontal force F that m exerts on M. F should be equal to the static friction force Fs in order to keep M remain resting.

Finally apply the equation: Fs < (static friction coef.) * N_M
Fs and N_M are expressed in terms of m, M and theta. Plug them into the above inequality and find m which satisfies the inequality for all values of theta in the range [0;pi] (or maybe [-pi/2 ; pi/2] depending which angle you choose).