A boy stands out at the end of the diving board, which is supported by two springs A and B, each having a stiffness of k = 15kN/m. In the position shown the board is horizontal. If the boy has a mass of 40 kg, determine the angle of tilt which the board makes with the horizontal after he jumps off.

Question

A boy stands out at the end of the diving board, which is supported by two springs A and B, each having a stiffness of k = 15kN/m. In the position shown the board is horizontal. If the boy has a mass of 40 kg, determine the angle of tilt which the board makes with the horizontal after he jumps off. Neglect the weight of the board and assume it is rigid.

Accepted Answer

Equations of Equilibrium: The spring force at A and B can be obtained directly by
summing moments about points B and A, respectively.

[latex]\hookrightarrow[/latex]+ [latex]\sum { M}_{ B }[/latex] = 0 ; [latex]{ F }_{ A } (1) - 392.4(3) = 0 { F }_{ A }[/latex] = 1177.2 N

[latex]\hookrightarrow[/latex]+ [latex]\sum { M}_{ A }[/latex] = 0 ; [latex]{ F }_{ B } (1) - 392.4(4) = 0 { F }_{ B }[/latex] = 1569.6 N

Spring Formula: Applying [latex]\Delta =\cfrac { f }{ k }[/latex] ,we have

[latex]{ \Delta }_{ A } = \cfrac { 1177.2 }{ 15 \left( { 10 }^{ 3 } ight) }[/latex] = 0.07848 m [latex]{ \Delta }_{ B } = \cfrac { 1569.6 }{ 15 \left( { 10 }^{ 3 } ight) } [/latex] = 0.10464 m

Geometry: The angle of tilt is

[latex]\alpha = { an }^{ -1 } \left( \cfrac { 0.10464+0.07848 }{ 1 } ight)[/latex] = 10.4°

Question : A boy stands out at the end of the diving board, which is su...

This Question has been Answered.

Already have an account?

Login