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Chapter 12: Q15P (page 346)

Question: ForcesF鈫�1,F鈫�2andF鈫�3 act on the structure of Fig. 12-33, shown in an overhead view. We wish to put the structure in equilibrium by applying a fourth force, at a point such as P. The fourth force has vector componentsF鈫�handF鈫�v . We are given that a = 2.0 m,b = 3.0m , c = 1 0 m , F鈫�1=20N,F鈫�2=10NandF鈫�3=5.0NFind (a) Fh , (b) Fv, and (c) d.

Short Answer

Expert verified

Answer

a.Fh=5.0Nb.Fv=30Nc.d=1.3m

Step by step solution

01

Understanding the given information  

a=2.0mb=3.0mc=1.0mF1=20NF2=10NF3=5.0N

02

Concept and formula used in the given question

By applying the equations of static equilibrium, you can get the equations in terms of unknown forces. By solving these equations, you can find the values of unknown forces and distance. The equations used are given below.

Static Equilibrium conditions:

鈭�Fx=0鈭�Fy=0鈭�蟿=0

03

(a) Calculation for the Fh

Using the given figure in the problem and applying static equilibrium conditions:
鈭�Fx=0Fh-F3=0路路路路路路(1)鈭�Fy=0Fv-F1-F2=0路路路路路路(2)鈭�=0Fv脳d-F2脳b-F3脳a=0路路路路路路(3)

From equation (1):

Fh-5=0

Hence, Fh-5=0

04

(b) Calculation for the  Fv

From equation (2):

Fv-20-10=0

Hence, Fv=30N

05

(c) Calculation for the  d

From equation (3):

30脳d-10脳3-5脳2=0d=1.3m

Hence, d = 1.3 m

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Most popular questions from this chapter

Figure 12-57 shows an approximate plot of stress versus strain for a spider-web thread, out to the point of breaking at a strain of 0.200. The vertical axis scale is set by values a=0.12 GN/m2, b=0.30 GN/m2, and c=0.80 GN/m2 . Assume that the thread has an initial length of 0.80 cm, an initial cross-sectional area of 8.0x10-12 m2, and (during stretching) a constant volume. Assume also that when the single thread snares a flying insect, the insect鈥檚 kinetic energy is transferred to the stretching of the thread. (a) How much kinetic energy would put the thread on the verge of breaking? What is the kinetic energy of (b) a fruit fly of mass 6.00 mg and speed 1.70 m/s and (c) a bumble bee of mass 0.388 g and speed 0.420 m/s ? Would (d) the fruit fly and (e) the bumble bee break the thread?

Figure 12-17 shows four overhead views of rotating uniform disks that are sliding across a frictionless floor. Three forces, of magnitude F, 2F, or 3F, act on each disk, either at the rim, at the center, or halfway between rim and center. The force vectors rotate along with the disks, and, in the 鈥渟napshots鈥� of Fig. 12-17, point left or right. Which disks are in equilibrium?

In Fig. 12-82, a uniform beam of length 12.0鈥尘 is supported by a horizontal cable and a hinge at angle 胃=50.0掳. The tension in the cable is 400鈥塏 .

In unit-vector notation, what are

(a) the gravitational force on the beam and

(b) the force on the beam from the hinge?

A uniform cube of side length 8.0鈥塩尘 rests on a horizontal floor.The coefficient of static friction between cube and floor is m. A horizontal pull P鈫�is applied perpendicular to one of the vertical faces of the cube, at a distance 7.0鈥塩尘above the floor on the vertical midline of the cube face. The magnitude of P鈫�is gradually increased. During that increase, for what values of渭 will the cube eventually (a) begin to slide and (b) begin to tip? (Hint:At the onset of tipping, where is the normal force located?)

Question: An automobile with a mass of 1360 kg has 3.05 m between the front and rear axles. Its center of gravity is located 1.78 m behind the front axle. With the automobile on level ground, determine the magnitude of the force from the ground on (a) each front wheel (assuming equal forces on the front wheels) and (b) each rear wheel (assuming equal forces on the rear wheels).
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