Question

The horizontal bar rises at a constant rate of three hundred mm/s causing peg P to ride in the quarter circular slot. When coordinate y reaches 150mm, find the v and a vectors for P. Hint: for a circle with origin shown x2+y2=r2. The radius of the slot is 300 mm.

Answer 1

Step-by-step explanation:

Given

Horizontal bar rises with 300 mm/s

Let us take the horizontal component of P be

`P_x=rcos\theta`

`P_y=rsin\theta`

where
`\theta`is angle made by horizontal bar with x axis

Velocity at y=150 mm

`150=300sin\theta`

thus
`\theta =30^(\circ)`

position of
`P_x=rcos\theta =300\cdot cos30=300* (√(3))/(2)`

`P_x=259.80 mm`

`P=259.80\hat{i}+150\hat{j}`

Velocity at this instant

`u_x=-rsin\theta =300* sin30=-150 mm/s`

`u_y=rcos\theta =300* cos30=259.80 mm/s`