Question

The small slider A is moved along the circular slot by a mechanism attached to the back side of the rectangular plate. For the slider position θ = 24° shown, determine the normal forces exerted at the small stops C and D. The unstretched length of the spring of constant k = 2.6 kN/m is R/5. The value of R is 20 mm, and the plate lies in a horizontal plane. Neglect all friction.

Before answering the question parts, draw a Free-Body diagram for the rectangular plate.

Chapter 3, Reserve Problem 3/043 Multistep The small slider A is moved along the circular slot by a mechanism attached to the back side of the rectangular plate. For the slider position = 240 shown, determine the normal forces exerted at the small stops C and D. The unstretched length of the spring of constant k = 2.6 kN/m is R/5. The value of R is 20 mm, and the plate lies in a horizontal plane. Neglect all friction. Before answering the question parts, draw a Free-Body diagram for the rectangular plate. Compare your diagram with that shown in Part 2. R 2 R 2 D R B А

Answer 1

ANSWER :
The free body diagram of the plate: Ro. R. Re. B. O P A The slider' A moves dong the circular s bt of the rectangeles plate The spring force p is on the side of stop e in the given position So the rectangular plate will rotate about pivot o towards stop D. The plate with touch the stop D and loose contact with stop c. Hence there will be at a normal reaction Roald and no recation force at C.

Consider the components of reaction at oas Ry and Ry in directions respectively Un- strecthed length of the spring is R/g and the stretched X and 4 length isr. a when body, under the action of a number of forces is in equilibrium ; the resultant force and resultant moment are both zero This algebraic sum of the components of forces alongs and yaxis, as well as algebraic sum of moments of the forces about any point are zero Mathematically, Ef x=0, {fy=0 and £M=0 consider the elongation s of the spring S=: R- R 3. alm 3 calculate the spring force using the following formaila.

2KR Р= kx S = kx 2 3 3. Here, k is the spring constant consider the normal force Rp atd Equate the sum of mo. moments of the forces acting on the plate about point o to zero EMOGO - pcose xRastne - psfnen (2-4.68) - Rearrange and simplity to find Ro. Thus Proso x Rsino + PainoxRx (5 +1-coso) Ro R R Rot 2 2 R R 2 3sino sino coso PxRx (spno cose + 2 R рх 3sing 2 Replace 2KR 3 =p KR. 3 sino Ro x 3 2 0 = kRsino Sustitute k=2.6x10² 03 ailm R=20x10 3m, 0-24

plate will touch the stop D Gl Rp = 12.6x103 N/m Dx (20x10 3.) xsin (240) = (2-6* 2023XS10 24" 21-150 N the normal force at stop Dis 21:1500 consider the normal force atc: The and loose contact with the stop c. the normal force at the stopc is at the stope is o' (zero)