Calculating Reaction Forces in Circular Motion

AI Thread Summary
A small object of mass 0.3 kg is moving in a hemispherical bowl with an angular velocity of 10 rad/s along a horizontal circular path of radius 20 cm. The reaction force on the object is analyzed by resolving forces into vertical and horizontal components, equating vertical forces to weight and horizontal forces to centripetal acceleration. The discussion highlights the challenge of finding the magnitude and direction of the reaction force, with a suggestion to treat the equations as simultaneous to solve for the unknowns. Dividing the equations can simplify the problem, leading to the calculation of the angle of the reaction force. The conversation emphasizes the importance of careful simplification in solving the equations.
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Homework Statement


A small object of mass 0.3 kg is moving inside a hemispherical bowl. It's angular velocity is 10 rad/s. The object travels in a horizontal circular path of radius 20 cm. Find the reaction on the object caused by the bowl and the radius if the bowl.

Homework Equations


Equations of circular motion..

The Attempt at a Solution


I tried resolving the reactions into two different directions. First, in the vertical direction. Because there is no acceleration in the vertical direction, F sin a (where a is the angle between the line of action of the reaction and the horizontal plane) is equal to the weight of the object (0.3 x g).

So F sin a = 0.3 x g

I did the same thing in the horizontal direction using F = ma. ( F = m x centripetal acceleration)

F cos a = 0.3 x w2 x 0.20.

However, I can't get beyond this. How can I find the reaction on the object?
(I don't think you're allowed to give g a numerical value such as 10 or 9.8 )
 
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You know both the horizontal and vertical component of the reaction force. How do you get the magnitude and the direction of this force then? ehild
 
mahela007 said:

Homework Statement


A small object of mass 0.3 kg is moving inside a hemispherical bowl. It's angular velocity is 10 rad/s. The object travels in a horizontal circular path of radius 20 cm. Find the reaction on the object caused by the bowl and the radius if the bowl.


Homework Equations


Equations of circular motion..


The Attempt at a Solution


I tried resolving the reactions into two different directions. First, in the vertical direction. Because there is no acceleration in the vertical direction, F sin a (where a is the angle between the line of action of the reaction and the horizontal plane) is equal to the weight of the object (0.3 x g).

So F sin a = 0.3 x g

I did the same thing in the horizontal direction using F = ma. ( F = m x centripetal acceleration)

F cos a = 0.3 x w2 x 0.20.

However, I can't get beyond this. How can I find the reaction on the object?
(I don't think you're allowed to give g a numerical value such as 10 or 9.8 )

You have two equations and two unknowns(Fand a)and you can treat these as simultaneous equations.One way is to divide equation one by equation two,the F will cancel and you will be left with an equation giving tan a(sin/cos=tan)
 
OK.. thanks
I did try dividing them. I seems I made a mistake in the simplification.
 

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