A 2-lb block rests on the smooth semicylindrical surface. An elastic cord having a stiffness k = 2 lb/ft is attached to the block at B and to the base of the semicylinder at point C. If the block is released from rest at A ( θ= 0° ), determine the unstretched length of the cord so that the block

Question

A 2-lb block rests on the smooth semicylindrical surface. An elastic cord having a stiffness k = 2 lb/ft is attached to the block at B and to the base of the semicylinder at point C. If the block is released from rest at A ( heta= 0° ), determine the unstretched length of the cord so that the block begins to leave the semicylinder at the instant heta = 45° . Neglect the size of the block.

Accepted Answer

[latex]+\swarrow \Sigma { F }_{ n }={ ma }_{ n };\quad \quad 2\sin { { 45 }^{ \circ }=\frac { 2 }{ 32.2 } (\frac { { v }^{ 2 } }{ 1.5 } ) } \ v=5.844ft/s\ { T }_{ 1 }+\Sigma { U }_{ 1-2 }={ T }_{ 2 }\ 0+\frac { 1 }{ 2 } (2){ [\pi (1.5)-{ l }_{ 0 }] }^{ 2 }-\frac { 1 }{ 2 } (2)[\frac { 3\pi }{ 4 } (1.5)-{ l }_{ 0 }]^{ 2 }-2(1.5\sin { { 45 }^{ \circ })=\frac { 1 }{ 2 } (\frac { 2 }{ 32.2 } ){ (5.844) }^{ 2 } } \ { l }_{ 0 }=2.77ft[/latex]

Question : A 2-lb block rests on the smooth semicylindrical surface. An...