Question

*Computer-Oriented Problems* 3/285. The two 0.2-kg sliders are connected by a light rigid bar of length L = 0.5 m. If the system is released from rest in the position shown with the spring unstretched, plot the speeds of A and B as functions of the displacement of B (with zero being the initial position). The 0.14-MPa air pressure acting on one 500=mm^2 side of slider A is constant. The motion occurs in a vertical plane. Neglect friction. State the maximum values of v_a and v_b and the position of B at which each occurs.

*3/285 The two 0.2-kg sliders are connected by a light rigid bar of length L = 0.5 m. If the system is released from rest in the position shown with the spring unstretched, plot the speeds of A and B as functions of the displacement of B (with zero being the initial position). The 0.14-MPa air pressure acting on one 500-mm" side of slider A is constant. The motion occurs in a vertical plane. Neglect friction. State the maximum values of va and Up and the position of B at which each occurs. -300 k = 1.2 kN/m Tommy 60°

Answer 1

From the given data,

Pressure acting on piston A (P)=0.14 MPa

area of piston A on which pressure is acting (A)= 500mm2

Net Force acting on pison A,

FA= P* A= 0.14 * 500 = 70N

We have mass of each pistion, m=0.2kg,

Acceleration of piston A,

FA 70 aA = m 02=350m/s2

Using this we can plot the acceleration diagram, From the acceleration diagram we can obtain the acceleration of the connecting rod. Using accleration of connecting rod we can find its velocity and plotting velocity diagram to find remaining velocity and displacement of spring.

Acceleration diagram 3.5 units 3.5 units 6.06 units B

From acceleration diagram,

Acceleration of slider B

ab = 350m/s2

Acceleration of Connecting rod

2$/u909 = TV

Vi= Va* TL = 17.406m/s

ie, Scale of vellcity diagram=(1212/4.502)= 2.8724(m/s)/units

Velocity triangle and accleration triangle are similar.

Velocity of slider A,

VA = 2.8724 * 3.5 = 10.05m/s

Velocity of slider B,

VB = 2.8724 * 3.5 = 10.05m/s

Force acting on the sliider B.

FB = m* dB

0.2 + 350 = sket?

2+0.2 + 350

substuting value of k will give the deflection of spring