The truss to analyse is loaded as shown below. The truss is supported by a frictionless pin at F and a frictionless roller at A. Determine: a) The magnitude of the reactions at the supports A and F. b) The force in member CD, HD and HG using the method of sections. Indicate if the members are in tension or compression. c) The force in member BH and FE using the method of joints. Indicate if the member is in tension or compression. Ω 100 .(m) B 50 kN 45° 45° D 30 kN A H 45° E 30 kN G Ω .(m)* Ω 100 100 (m)-

Hanging from the ceiling over a baby bed, well out of baby’s reach, is a string with plastic shapes, as shown here. The string is taut (there is no slack), as shown by the straight segments. Each plastic shape has the same mass m , and they are equally spaced by a distance d , as shown. The angles labeled describe the angle formed by the end of the string and the ceiling at each end. The center length of sting is horizontal. The remaining two segments each form an angle with the horizontal, labeled . Let T1 be the tension in the leftmost section of the string, T2 , be the tension in the section adjacent to it, and T3 be the tension in the horizontal segment. (a) Find an equation for the tension in each section of the string in terms of the variables m,g , and . (b) Find the angle in terms of the angle . (c) If =5.10 , what is the value of ?(d) Find the distance x between the endpoints in terms of d and .

In order to lift a shovelful of dirt, a gardener pushes downward on the end of the shovel and pulls upward at distance l2 from the end, as shown below. The weight of the shovel is mg and acts at the point os application of F2 . Calculate the magnitudes of the forces F1 and F2 as functions of l1 , l2 , mg, and the weight W of the load. Why do your answers not depend on the angle that shovel makes with the horizontal?

In order to get his car out of the mud, a man ties one end of a rope to the front bumper and the other end to a tee 15 m away as shown below. He then pulls on the center of the rope with a force of 400 N, which causes its center to be displaced 0.30 m, as shown. What is the force of the rope on the car?