Question

A mass of feed-corn is hauled up the
silo elevator on the straight path from O to A. When
it is at the midpoint, its speed is 2 ft/s and the
acceleration up the elevator is 0.5 ft/s2. (a) Express
the velocity and acceleration of the mass at this point
in terms of its cylindrical components (vector form).
(b) Express the velocity and acceleration of the mass
at the same point in terms of its cylindrical
components (vector form), if the mass is moving
down the elevator instead of up and accelerating
towards O.

v.a 63 ft 0 21 ft 35 ft

Answer 1

OB = squareroot 35^2 + 21^2 = 49 = 0.382 ft tan theta = 63/40.82 theta = 57.06 degree V_2 = component in z direction = U sin theta = 2 sin 5706 V_2 = 1.6784 tildeequalto 1.68 ft/s V_1 = velocity in the plane xy = V cos theta = 2 cos 5706 = 1.09 ft/s tan theta_1 = 21/35 = 3/5 theta_1 = 30.964 degree V_g = component in y direction = V_1 cos 30.964 = 0.935 ft/s V_n = component in n direction = v_1 sin 30.964 = 0.561ft/s V^rightarrow = 0.561 icirc + 0.935 jcirc + 1.68 Rcirc a_2 = component in 2 displacement n = 0.5 sin 57.07 = 0.42ft/s^2 a_1 = acceleration in plane xy = 0.5 cos 57.06 = 0.272ft/s^2 a_y = component in y direction = a_1 cos 30.964 = 0.233ft^2 a_x = component in x direction = a_1 sin 30.964 = m 0.139 ft/s^2 a^rightarrow = 0.1399