Question

2. (Chapter 13: Use rectangular coordinates)
The sliders A and B are connected by a light rigid bar of length l = 0.5 m and move with negligible friction in the horizontal slots shown (see Figure 2). For the position where xA = 0.4 m, the velocity of A is vA = 0.9 m/s to the right. At this instant
(a) draw the free-body-diagrams sliders A and B,
(b) determine the acceleration of the slider B, and
(c) determine the force in the bar.

Answer 1

Draw the schematic diagram of the sliders.

Calculate the length .

Apply Pythagoras formula to calculate the length of the slider.

Here, l is the length of the bar.

Substitute 0.4 m for and 0.5 m for l.

Again, apply Pythagoras formula to obtain the relation for the length of the slider.

…… (1)

Here, length of the rigid bar is, distance of slider is and distance of slider is.

Obtain the relation the velocity of slider by differentiating equation (1) with respect to t.

…… (2)

Substitute for, for and for.

Obtain the relation for the acceleration of slider by differentiating equation (2).

Consider equation (2),

Differentiate the equation with respect to t.

Substitute for, for, for and for.

…… (3)

Draw the free body diagram of slider.

Calculate the force acting along-direction.

Here, angle of inclination is and mass of slider is.

Substitute for and for in above equation.

…… (4)

Draw the free body diagram of slider .

Calculate the force acting along-direction.

Here, angle of inclination is and mass of slider is.

Substitute for and for.

…… (5)

Calculate the acceleration of slider by substituting equation (5) in equation (4).

Substitute equation (3) for .

Substitute for .

Therefore, the acceleration of slider is.

Calculate the acceleration of slider.

Thus, from equation (3),

Rewrite the equation as,

Substitute for.

Therefore, the acceleration of slideris

Calculate the tension in the bar.

Substitute for .

Therefore, the tension in the bar is.