A person of mass M is sitting on a swing of length L and swinging with and an angular amplitude θ 0 . If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance l   l < < L , is close to:

Question

A person of mass M is sitting on a swing of length L and swinging with and an angular amplitude &#952; 0 . If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance l &#160; l &#60; &#60; L , is close to:

Aicharya · Accepted Answer

From angular momentum conservation M V 0 L = M V ( L - l ) V = V 0 L L - l Now W = M g l + 1 2 M V 0 2 L L - l 2 - V 0 2 Since l &#8810; L W = M g l + 1 2 M V 0 2 1 - l L - 2 - V 0 2 = M g l + 1 2 M V 0 2 1 + 2 l L - V 0 2 = M g l + M V 0 2 l L From SHM V 0 = &#969; A = g L &#215; L &#952; 0 = g L &#952; 0 Using this W = M g l + M g L &#215; &#952; 0 2 &#215; l L W = M g l 1 + &#952; 0 2

A person of mass M is sitting on a swing of length L and swinging with and an angular amplitude θ 0 .…

Solution

A person of mass M is sitting on a swing of length L and swinging with and an angular amplitude &#952; 0 .…

Solution

A person of mass M is sitting on a swing of length L and swinging with and an angular amplitude θ 0 .…