Statics and Strength of Materials HW1 part 1

Statics and Strength of Materials HW1 part 1
1) A vector V has a magnitude of 20 units and lies in the x-y plane. If its direction cosine with respect to the y-axis is -0.6 and if its xcomponent is positive, write the vector expression for V using unit vectors i and j. Write the unit vector n in the direction of V.
2) Calculate the following operations by graphically and analytically.
a) 2V1+V2
b) V2-2V1
Fig 2
3) a) If the two equal tensions T in the pulley cable together produce a force of 5 kN on the
pulley bearing, calculate T.
b) If the equal tensions T in the pulley cable are 400 N, express in vector notation the
force R exerted on the pulley by the two tensions. Determine the magnitude of R.
Fig 3
4) The 600-N force applied to the bracket at A is to be replaced
by two forces, Fa in the a-a direction and Fb in the b-b
direction, which together produce the same effect on the
bracket as that of the 600-N force. Determine Fa and Fb.
Fig 4
5) Combine the two forces shown acting on the A-frame into a single force R. Express
R in vector notation using unit vectors i and j, and determine its magnitude R and the
angle q it makes with the x-axis. If R were to be applied at a point D on member AB,
find the distance s from A to D.
Fig 5
6) Two cylindrical body positioned in the container having rectangular prism.
Calculate all reaction forces acting on each body.
Fig 6
7)Aforce system is shown in figure.
a) Find the resultant R.
b) Find the line of the resultant.
c) Translate R to the point O.
d) Find the components of the R along the m-m direction and the direction
passing through the pointsA(-2,1) and (1,6).
Fig 7
8) Find the components of the 10-kN force P in the I, II and III directions.
Fig 8
9) The 50-kg homogeneous smooth sphere rests on the 30-deg incline A and
bears against the smooth vertical wall B. Calculate the contact forces at A
and B.
Fig 9
10) The uniform bar AB has a mass of 50-kg and supports the 200-kg load at
A. Calculate the tension in the supporting cable and the magnitude FB of the
force supported by the pin at B.
Fig 10
11) Determine the force P required to begin rolling the uniform cylinder of
mass m over the obstruction of height h.
Fig 11
12)Soil pressure acting on the concrete retaining wall is presented as a
loading per foot length of wall. If concrete has a specific weight of 25 kN/m3,
determine the magnitudes of the soil distribution, w1 and w2 and the frictional
force F for equilibrium.
Fig 12
Fig 13
13) If neither the pin at A nor the roller at B can support a load no greater than 6 kN, determine the maximum intensity of the
distributed load w, measured in kN/m, so that failure of a support does not occur.
14 and 15) Determine the coordinates of the centroid xc and yc of the shaded area.
y
h
4 cm
10 cm
Fig 14
10 cm
10 cm
x
Fig 15
Due date : 19 March 2015
! This is the first part of the first homework. It must be done fully and written
properly with a cover page.