Question

slider block b moves to the right with a constant velocity of 300 mm/s. determine (a) the velocity of slider block a, (b) the velocity of portion c of the cable, (c) the velocity of portion d of the cable, (d) the relative velocity of portion c of the cable with respect to slider block a.

Explanation:

Step1: Analyze the cable - pulley system

Let the velocity of slider block B be \(v_B = 300\space mm/s\). Assume the length of the cable is constant. If we consider the kinematics of the cable - pulley system, for a simple pulley - cable arrangement, the velocities of different points on the cable are related based on the geometry of the system.

Step2: Determine the velocity of portion C with respect to ground

Since the cable is inextensible and assuming no slippage on the pulleys, if block B moves to the right with a velocity \(v_B\), the velocity of portion C of the cable (which is directly connected to the motion of block B in a non - stretched part of the cable) has the same velocity as block B. So \(v_C=v_B = 300\space mm/s\) to the right.

Step3: Determine the velocity of portion D of the cable

The velocity of portion D of the cable is also equal to the velocity of block B because of the inextensibility of the cable and the nature of the pulley arrangement. So \(v_D = v_B=300\space mm/s\) to the right.

Step4: Determine the relative velocity of portion C with respect to slider block A

Let the velocity of slider block A be \(v_A\). The relative velocity of portion C with respect to slider block A, \(v_{C/A}=v_C - v_A\). If we assume block A is stationary (\(v_A = 0\)), then \(v_{C/A}=300\space mm/s\) to the right.

Answer:

(a) The velocity of portion C of the cable is \(300\space mm/s\) to the right.
(b) The velocity of portion C of the cable is \(300\space mm/s\) to the right.
(c) The velocity of portion D of the cable is \(300\space mm/s\) to the right.
(d) If slider block A is stationary, the relative velocity of portion C with respect to slider block A is \(300\space mm/s\) to the right.