ENGINEERING MECHANICS

ASSIGNMENT 3

1

A boat is suspended on two identical devits like ABC whcihc is pivoted at A and supported by a guide at B (Fig A). Determine the reactions R(A) and R(B) at points A and B if the vertical load transmitted to each davit at C is 4272 N. Friction in the guide at B should b neglected.

2

A horizontal beam AB is hinged to a vertical wall at A and supported at its midpoint C by a tie rod CD as shown in Fig G. Find the tension S in the tie rod and the reaction at A due to a vertical load P applied at B.

3

A horizontal prismatic bar AB of negligible weight and length l, is hinged to a vertical wall at A and supported at B by a tie rod BC that makes the angle α with the horizontal (Fig H). A weight P can have any position along the bar as defined by the distance x from the wall. Determine the tensile force S in the tie bar.

4

A ball of weight Q and radiue r is attached by a string AD to a vertical wall AB, as shown in Fig C. Determine the tensile force S in the string and the pressure R(b) against the wall at B if Q= 35.6 N, r= 75mm, AB =100mm. Neglect the friction at wall.

5

A bar AB hinged to the foundation at A and supported by a strut CD is subjected to a horizontal 50 kN load at B as shown in the figure M. Find graphically the tensile force S in the strut and the reaction R(A) at A.

6

Find graphically the reactions R(A) and R(B) induced at the supports A and B of the right angled bar ACB supported as shwon in the Fig N and subjected to a vertical load P applied at the midpoint of AC

ASSIGNMENT 4

1

A beam AB hinged at A and supported at B by a vertical bar BC, is subjected to the action of a force P applied as shown in Fig C. Assuming ideal hinges at A, B and C, find the force S produced in the bar BC. Neglect the weight of the beam.

2

A long ladder supported at A and B as shown in Fig D, a vertical load W can have any position as defined by the distance a from the bottom. Neglecting friction, determine the magnitude of the reaction R(B) at B. Neglect the weight of the ladder

3

A rocker of weight W having a circular shoe AB of radius a and with cent at O rests on a horizontal surface and is pulled by a horizontal force P applied at O, as shown in the Fig M. Find the position of the equilibrium, as defined by the angle α, which the rocker will assume if its center of gravity is at C, distance b from O along the bisecting radius OE.

4

A rpismatic bar AB of weight Q and length l is hinged at A and supported at B by an elstic spring that passes over a pulley C. The spring is fixed at the other end D as shown in Fig P. The distance between the hinge A and the pulley C is equal to the length l of the bar AB. The stiffeness of the spring is k and the spring is unstretched when the bar AB is horizontal. Find the configuration of equilibrium of the system as defined by the angle α, which the bar makes with the horizontal sa shown in the figure in terms of Q, k, l.

5

A vertical prismatic bar AB of negligible weight and length l, is hinged to a cylinder of radius r at A and suported at D by an elastic spring CD (Fig O). The stiffeness of the spring is k and the spring is undeformed when α= 00. The horizontal force P is applied to the bar AB at B as shown in the figure. Find the position of the equilibrium, as defined by angle α, in terms of P, K, l and r.

6

A prismatic bar AB of weight P is hinged at point A and attached to a spring at point B as shown in Fig Q. The stiffness of a spring is k and the spring is undeformed when anble α= 900. Find the angle α corresponding to equilibrium in terms of P,k and l as shwon in figure.