contestada

Pin p is constrained to move along the curve defined by the lemniscate r=(4sin2θ)ft.if the slotted arm oa rotates counterclockwise with a constant angular velocity of θ˙ = 1.0 rad/s , determine the magnitude of the velocity of peg p when θ = 59 ∘.

Respuesta :

position of the peg is given by the equation

[tex]r = 4 sin2\theta[/tex]

now the rate of change in position is given as

[tex]v = \frac{dr}{dt}[/tex]

[tex]v = \frac{d}{dt}(4 sin2\theta)[/tex]

[tex]v = 8cos2\theta*\frac{d\theta}{dt}[/tex]

[tex]v = 8 cos2\theta*\omega[/tex]

given that

[tex]\omega = 1 rad/s[/tex]

[tex]\theta = 59 degree[/tex]

now we have

[tex]v = 8*cos(2*59)* 1 = -3.76 m/s[/tex]

so its speed will be 3.76 m/s in magnitude