Question

Find the minimum height h that will allow a solid cylinder of mass m and radius rcyl to loop the loop of radius rloop. Express h in terms of the radius rloop of the loop.

Answer 1

Answer: check explanation

Explanation:

We know that V= √gr-----------------------------------------------------------------------------------------------------------------------(**)

Energy at the top of the loop;

= 1/2×m×V^2 + mg(2r)-------------------------------------------------------------------(1).

Potential energy= mgh-------------------------------------------------------------------(2).

Equating equation (1) and equation (2), we have;

=> 1/2×m×V^2 + mg(2r)= mgh-------------------------------------------------------(3).

=> 1/2(gr)+g(2r) = gh------------------------------------------------------------------(4).

Also, mg =mV^2/R-r---------------------------------------------------------------------(5).

Therefore, h in terms of the radius rloop of the loop is;

h=5/2× r_loop.

Answer 2

The minimum height that a solid cylinder will travel from a given position is, h = 6v²/8g.

Minimum height traveled by the solid cylinder

The minimum height that a solid cylinder will travel is determined by applying the principle of conservation of mechanical energy as shown below;

K.E = P.E

¹/₂mv² + ¹/₂Iω² = mgh

where;

• I is the moment of inertia of a solid cylinder = ¹/₂mr²
• ω is angular speed = v/r

¹/₂mv² + ¹/₂(¹/₂mr²)(v/r)² = mgh

¹/₂v² + ¹/₄v² = gh

6v² = 8gh

h = 6v²/8g

where;

• v is the speed of the solid cylinder at the bottom of its path of motion.

Thus, the minimum height that a solid cylinder will travel from a given position is, h = 6v²/8g.

Learn more about moment of inertia of solid cylinder here: https://brainly.com/question/14595503