Answer:
Velocity components
V_r = -16.28 m/s
V_z = -22.8 m/s
V_q = 0 m/s
Acceleration components
a_r = -4.07 m/s^2
a_z = -5.70 m/s^2
a_q = 0 m/s^2
Explanation:
Given:
- The diagram missing is attached.
- The speed of the washer v_o = 28 m/s
- The acceleration of washer a_o = 7 m/s^2
Find:
Express the velocity and acceleration of the washer at this point in terms of its cylindrical components.
Solution:
- From figure, compute the radial position r of washer in x-y plane:
r = sqrt ( 300^2 + 400^2 )
r = 500 mm
- From figure, compute the Length L of along the OA direction:
L = sqrt ( 500^2 + 700^2 )
r = 860 mm
- The radial and vertical components of velocity are:
V_r = V_o*cos(Q)
V_z = V_o*sin(Q)
Where, Q is the angle between OA and vector r.
V_r = 28*r/L = 28*500 / 860
V_r = -16.28 m/s
V_z = 28*700/L = 28*700 / 860
V_z = -22.8 m/s
V_q = 0 m/s
- The radial and vertical components of acceleration are:
a_r = a_o*cos(Q)
a_z = a_o*sin(Q)
Where, Q is the angle between OA and vector r.
a_r = 7*r/L = 7*500 / 860
a_r = -4.07 m/s^2
a_z = 7*700/L = 7*700 / 860
a_z = -5.70 m/s^2
a_q = 0 m/s^2
