A constant horizontal force P=150 lb is applied to the linkage as shown. With th

Question

A constant horizontal force P=150 lb is applied to the linkage as shown. With the 30-lb ball initially at rest on its support with theta=60 degrees, calculate the velocity v of the ball as theta approaches zero where the ball reaches its highest position

A constant horizontal force P=150 lb is applied to the linkage as shown. With the 30-lb ball initially at rest on its support with theta=60 degrees, calculate the velocity v of the ball as theta approaches zero where the ball reaches its highest position

Explanation / Answer

when theta approaches zero the link connecting the ball will be pepndicular

the work done by the force P = P * 9 *sin(theta) =1169.13

the potential energy of the ball when its vertical = m* g*(18-18cos(theta)) = 104279.3

the potential energy is greater at the highest point is greater than the work input so it will never reach the point

the kinetic energy of the ball = 1/2m*v^2

applying the conservation of energy

work = P.E + KE

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