Ask Question
5 December, 00:46

The sliders A and B are connected by a light rigid bar of length l = 20 in. and move with negligible friction in the slots, both of which lie in a horizontal plane. For the position where xA = 16 in., the velocity of A is vA = 3 ft/sec to the right. Determine the acceleration of each slider and the force in the bar at this instant.

+3
Answers (1)
  1. 5 December, 02:47
    0
    Given:

    - The Length of the rigid bar L = 20 in

    - The position of slider a, x_a = 16 in

    - The position of slider b, y_b

    - The velocity of slider a, v_a = 3 ft / s

    - The velocity of slider b, v_b

    - The acceleration of slider a, a_a

    - The acceleration of slider b, a_b

    Find:

    -Determine the acceleration of each slider and the force in the bar at this instant.

    Solution:

    - The relationship between the length L of the rod and the positions x_a and x_b of sliders A & B is as follows:

    L^2 = x_a^2 + y_b^2 ... 1

    y_b = sqrt (20^2 - 16^2)

    y_b = 12

    - The velocity expression can derived by taking a derivation of Eq 1 with respect to time t:

    0 = 2*x_a*v_a + 2*y_b*v_b

    0 = x_a*v_a + y_b*v_b ... 2

    0 = 16*36 + 12*v_b

    v_b = - 48 in / s = - 4 ft/s

    - Similarly, the acceleration expression can be derived by taking a derivative of Eq 2 with respect to time t:

    0 = v_a^2 + x_a*a_a + v_b^2 + y_b*a_b

    0 = 9 + 4*a_a/3 + 16 + a_b

    4*a_a/3 + a_b = - 25

    4*a_a + 3*a_b = - 75 ... 3

    - Use dynamics on each slider. For Slider A, Apply Newton's second law of motion in x direction:

    F_x = m_a*a_a

    P - R_r*16/20 = m_a*a_a

    - For Slider B, Apply Newton's second law of motion in y direction:

    F_y = m_b*a_b

    - R_r*12/20 = m_b*a_b

    - Combine the two dynamic equations:

    P - 4*m_b*a_b / 3 = m_a*a_a

    3P = 3*m_a*a_a + 4*m_b*a_b ... 4

    - Where, P = Is the force acting on slider A

    P, m_a and m_b are known quantities but not given in question. We are to solve Eq 3 and Eq 4 simultaneously for a_a and a_b.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “The sliders A and B are connected by a light rigid bar of length l = 20 in. and move with negligible friction in the slots, both of which ...” in 📘 Engineering if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers