it starts moving from the bottom of the circle to the left and up (clockwise). When it reaches the point corresponding to 9 o'clock it presses the rail with the force 3mg. The mass of the body is m, the radius of the cicrle is R and the gravity acceleration is g.
A. What are the forces acting on the body at the point of 9 o'clock and what is its speed at this point?
B. What is the initial speed of the body at the bottom of the circle (6 o'clock point)?
A. What are the forces acting on the body at the point of 9 o'clock and what is its speed at this point?
B. What is the initial speed of the body at the bottom of the circle (6 o'clock point)?
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a. the forces acting on the particle are weight acting down, and the normal force acting horizontally toward the center of the circle
the normal force must balance the centripetal force, so we have that
m v^2/r = 3 m g or v = Sqrt[3 g r]
b) assuming conservation of energy holds, then the KE at the bottom equals KE at 9:00 plus the PE at 9:00, or
1/2 m vbottom^2 = 1/2 m (3 g r) + m g r
v bottom = Sqrt[5 g r]
the normal force must balance the centripetal force, so we have that
m v^2/r = 3 m g or v = Sqrt[3 g r]
b) assuming conservation of energy holds, then the KE at the bottom equals KE at 9:00 plus the PE at 9:00, or
1/2 m vbottom^2 = 1/2 m (3 g r) + m g r
v bottom = Sqrt[5 g r]