The Question is:
A guide with a vertical slot is given a horizontal motion of
x=200cos(0.3t), where x is in mm, t is in seconds and (0.3t) in
radians. The guide controls the motion of pin P, which is also
constrained to move along a fixed parabolic slot as shown below.
The parabolic slot has a shape given by the equation
y=x(squared)/200, where y is in mm.
For the instant where t=6.0seconds,
(a) Determine the position, velocity and acceleration of P in
X-Y components.
(b) Determine the rate at which the speed of P is changing.
(c) Determine the instantaneous radius of curvature of the
path.
Forget the diagram, with your level of 'awesomeness', these
should be enough. : D
a) y=(x^2)/200 ---> Sub in x = 200cos(0.3t) ---> y=
200[cos(0.3t) ]^2
Therefore position of P, (x,y) given by x=200 cos(0.3t) ,
y=200[cos(0.3)]^2
Velocity of P, (vx, vy), given by vx = dx/dt , vy = dy/dt (sub
in x and y from above)
acceleration of P, (ax, ay) given by ax= dvx/dt, ay = dvy/dt
(sub in vx and vy from above)
b) rate at which speed of P is changing = rate of change of
velocity. Simply use pythagaros theorem with answer = sqrt( ax^2 +
ay^2)
c) acceleration = v^2 /r
acceleration = answer from part b
v = sqrt(vx^2 + vy^2)
