A 4-lb ball B is traveling around in a circle of radius r1 = 3 ft with a speed (vB)1 = 6 ft/s. If the attached cord is pulled down through the hole with a constant speed vr = 2 ft/s, determine the ball’s speed at the instant r2 = 2 ft. How much work has to be done to pull down the cord? Neglect

Question

A 4-lb ball B is traveling around in a circle of radius{ r }_{ 1 }= 3 ft with a speed { ({ v }_{ B }) }_{ 1 } = 6 ft/s. If the attached cord is pulled down through the hole with a constant speed{ v }_{ r }= 2 ft/s, determine the ball’s speed at the instant{ r }_{ 2 }= 2 ft. How much work has to be done to pull down the cord? Neglect friction and the size of the ball.

Accepted Answer

[latex]{ H }_{ 1 }={ H }_{ 2 }\ \frac { 4 }{ 32.2 } (6)(3)=\frac { 4 }{ 32.2 } { v }_{ heta }(2)\ { v }_{ heta }=9ft/s\ { v }_{ 2 }=\sqrt { { 9 }^{ 2 }+{ 2 }^{ 2 } } =9.22ft/s\ { T }_{ 1 }+\Sigma { U }_{ 1-2 }={ T }_{ 2 }\ \frac { 1 }{ 2 } (\frac { 4 }{ 32.2 } )({ 6) }^{ 2 }+\Sigma { U }_{ 1-2 }=\frac { 1 }{ 2 } (\frac { 4 }{ 32.2 } )({ 9.22) }^{ 2 }\ \Sigma { U }_{ 1-2 }=3.04ft\cdot lb[/latex]

Question : A 4-lb ball B is traveling around in a circle of radius r1 =...