A pin is forced to move along a parabola shaped guide by a connected collar that

Question

A pin is forced to move along a parabola shaped guide by a connected collar that moves along the x-axis only. When x = 1.8m the velocity and acceleration of the collar are: v_x = 1.1 m/s and a_x = 1.2m/s^2 respectively. The parabolic guide is described by y = -l.25 x^2 + 5x.where both x and y are in units of metres. (a) What is the y-component of velocity.V_y at this instant? (b) What is the magnitude of the acceleration at this instant? (c) What is the normal component of the acceleration at this instant?

Explanation / Answer

(a) vy = dy/dt = -2.5xvx + 5vx

At x = 1.8 m,

vy = (-2.5 * 1.8 * 1.1) + (5 * 1.1) = 0.55 m/s

(b) ay = dvy/dt = -2.5(vx2 + xax) + 5ax

At x = 1.8 m,

ay = -2.5[1.12 + (1.8 * 1.2)] + (5 * 1.2) = -2.4 m/s2

Magnitude of acceleration, a = (ax2 + ay2)1/2 = [1.22 + (-2.4)2]1/2 = 2.7 m/s2

(c) Normal component of acceleration, ay = -2.4 m/s2

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