17. A ladder of length L is slipping with its ends against a vertical

1.	17. A ladder of length L is slipping with its ends against a vertical wall and a horizontal floor. At acertainmoment, the speed of the end in contact with tre horizontal floor is v and the ladder makes an anglea 300 with the horizontal. Then the speed of the ladder's center must be :
Answer» LetABbe the ladder with end B on the floor. let G be its center. When a body is having both translation and rotation it can be thought of as rotating about instantaneous center. It is changing continuously and is obtained by the intersection of perpendiculars to the direction of motion at any two points on the body, In this caseAis moving vertically andBis moving horizontally. If we draw a horizontal line fromAand a vertical line fromBBthey intersect atII. IB=lsin30° Now instantaneous angular velocityω=vB/ IB=vG/ IG It can be seen thatIB=l/ 2 vb=v Sov/ l/2 =vG/ lsin30∘vl2= from which vG=v

17. A ladder of length L is slipping with its ends against a vertical wall and a horizontal floor. At acertainmoment, the speed of the end in contact with tre horizontal floor is v and the ladder makes an anglea 300 with the horizontal. Then the speed of the ladder's center must be :

Answer»

LetABbe the ladder with end B on the floor. let G be its center. When a body is having both translation and rotation it can be thought of as rotating about instantaneous center. It is changing continuously and is obtained by the intersection of perpendiculars to the direction of motion at any two points on the body,

In this caseAis moving vertically andBis moving horizontally.

If we draw a horizontal line fromAand a vertical line fromBBthey intersect atII.

IB=lsin30°

Now instantaneous angular velocityω=vB/ IB=vG/ IG

It can be seen thatIB=l/ 2

vb=v

Sov/ l/2 =vG/ lsin30∘vl2=

from which

vG=v

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