Pegs A and B are restricted to move in the elliptical slots...

Pegs A and B are restricted to move in the elliptical slots due to the motion of the slotted link. If the link moves with a constant speed $v = 10 m/s$, determine the velocity and acceleration vectors of peg A when $x = 1 m$. Hint: Derivatives, chain rule, you know the drill. Careful! Pegs have $v_x$ and $v_y$ components (and what does $v_x$ have to be?)!

Transcript

00:01 Pags a and b are stricter to move in elliptical slots due to the motion of the slot that link moves to the constant speed of 10 meters for a second determine the velocity and acceleration vector of bag a when x is equal to 1 meter so first we're going to differentiate the equation for the ellipse x squared over 3 plus y squared and by 6 is equal to 1 we're respect to the time so we have x but x is going to be a function of the time so we're going to use the chain rule this is 2x different ships on what is outside first and multiplied by the derivative of the inside which is the x to t divided by 3 plus 2 y times d y d x x x x and b divided by 6 is equal to 1 so so we just need to x to t for the velocity and the y the t for the velocity and the y direction.

01:09 So we have 2x vx divided by 3 plus 2y v .y by 6 which is just 1 of 3.

01:22 Y v .y divided by 3 is equal to this will be 0.

01:29 So we're giving that the link moves with the constant speed of 10 meters per second.

01:32 So vx is going to be 10 meters per second.

01:34 That's in the horizontal direction.

01:36 Just move the pink the peg moves horizontally so as well as the ellipse on pegs are going to move horizontally with that same velocity because they are together so we have two x times 10 divided by 3 and also don't forget that we have on the x is equal to one meter so we can just see that in two times one times this x is equal to 1 v x is equal to 10 and also can find y from this equation we have xx plus y squared is equal to 1 so have 1 squared over 3 plus y squared over 6 is equal to 1 using the calculator y will be equal to 2 so bringing that here we have plus 2 times v y over 3 is equal to 0 so solving for v y in this equation this will get us minus 10 in 1 times the second so now now we can solve for the magnetism of velocity.

02:54 V is equal to the square of v x squared plus vy squared, which is simply square of 10 squared plus minus 10 squared this is equal to 10 root 2 meters per second.

03:15 And now for the acceleration, we can differentiate the velocity equation again to find the acceleration...

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