VECTOR MECHANICS FOR ENGINEERS: STATICS
VECTOR MECHANICS FOR ENGINEERS: STATICS
12th Edition
ISBN: 9781260912814
Author: BEER
Publisher: MCG
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Textbook Question
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Chapter 10.1, Problem 10.5P

A spring of constant 15 kN/m connects points C and F of the linkage shown. Neglecting the weight of the spring and linkage, determine the force in the spring and the vertical motion of point G when a vertical downward 120-N force is applied (a) at point C, (b) at points C and H.

Chapter 10.1, Problem 10.5P, A spring of constant 15 kN/m connects points C and F of the linkage shown. Neglecting the weight of

Fig. P10.5 and P10.6

(a)

Expert Solution
Check Mark
To determine

Find the force in the spring and the vertical motion of point G when a vertical load of 120N force is applied at point C.

Answer to Problem 10.5P

The force in the spring is 60N(C)_.

The vertical motion of point G is 8mm()_.

Explanation of Solution

Given information:

The spring constant is k=15kN/m.

Calculation:

Show the free-body diagram of the spring assembly as in Figure 1.

VECTOR MECHANICS FOR ENGINEERS: STATICS, Chapter 10.1, Problem 10.5P

Write the relation of the deflections at point G, H, F, E, D with C as follows;

yG=4yC;δyG=4δyC

yH=4yC;δyH=4δyCyF=3yC;δyF=3δyCyD=2yC;δyD=2δyCyE=2yC;δyE=2δyC

The deflection Δ of the spring is;

Δ=yFyC=3yCyC=2yC

Assume the spring force Q is in tension.

Find the force in the spring Q using the relation.

Q=+kΔ

Here, the spring constant is k.

Substitute 15kN/m for k and 2yC for Δ.

Q=15(2yC)=30yC (1)

Use the virtual work principle:

δU=0CδyC+QδyCQδyFFδyFHδyHEδyE=0

Here, E=0;F=0;H=0;C=120N

Substitute 120 N for C, 3δyC for δyF, 0 for F, 0 for H, 4δyC for δyH, 0 for E, and 2δyC for δyE.

120δyC+QδyCQ(3δyC)(0)(3δyC)(0)(4δyC)(0)(2δyC)=0120+Q3Q000=02Q=120Q=60N

Q=60N(C)

The spring force Q is in compression. The assumption is incorrect.

Therefore, the force in the spring is 60N(C)_.

Substitute –60 N for Q in Equation (1).

60=30yCyC=2mm

Find the vertical motion (yG) of point G using the relation.

yG=4yC

Substitute –2 mm for yC.

yG=4(2)=8mm=8mm()

Therefore, the vertical motion of point G is 8mm()_.

(b)

Expert Solution
Check Mark
To determine

Find the force in the spring and the vertical motion of point G when a vertical load of 120N force is applied at point C and H.

Answer to Problem 10.5P

The force in the spring is 300N(C)_.

The vertical motion of point G is 40mm()_.

Explanation of Solution

Given information:

The spring constant is k=15kN/m.

Calculation:

Use the virtual work principle:

δU=0CδyC+QδyCQδyFFδyFHδyHEδyE=0

Here, E=0;F=0;H=120N;C=120N

Substitute 120 N for C, 3δyC for δyF, 0 for F, 120 N for H, 4δyC for δyH, 0 for E, and 2δyC for δyE.

120δyC+QδyCQ(3δyC)(0)(3δyC)(120)(4δyC)(0)(2δyC)=0120+Q3Q04800=02Q=600Q=300N

Q=300N(C)

The spring force Q is in compression. The assumption is incorrect.

Therefore, the force in the spring is 300N(C)_.

Substitute –300 N for Q in Equation (1).

300=30yCyC=10mm

Find the vertical motion (yG) of point G using the relation.

yG=4yC

Substitute –10 mm for yC.

yG=4(10)=40mm=40mm()

Therefore, the vertical motion of point G is 40mm()_.

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Chapter 10 Solutions

VECTOR MECHANICS FOR ENGINEERS: STATICS

Ch. 10.1 - Prob. 10.11PCh. 10.1 - Knowing that the line of action of the force Q...Ch. 10.1 - Solve Prob. 10.12 assuming that the force P...Ch. 10.1 - The mechanism shown is acted upon by the force P....Ch. 10.1 - Prob. 10.15PCh. 10.1 - 10.15 and 10.16 Derive an expression for the...Ch. 10.1 - A uniform rod AB with length l and weight W is...Ch. 10.1 - The pin at C is attached to member BCD and can...Ch. 10.1 - For the linkage shown, determine the couple M...Ch. 10.1 - For the linkage shown, determine the force...Ch. 10.1 - A 4-kN force P is applied as shown to the piston...Ch. 10.1 - A couple M with a magnitude of 100 Nm isapplied as...Ch. 10.1 - Rod AB is attached to a block at A that can...Ch. 10.1 - Solve Prob. 10.23, assuming that the 800-N force...Ch. 10.1 - Prob. 10.25PCh. 10.1 - Determine the value of corresponding to...Ch. 10.1 - Prob. 10.27PCh. 10.1 - Determine the value of corresponding to...Ch. 10.1 - Prob. 10.29PCh. 10.1 - Two rods AC and CE are connected by a pin at Cand...Ch. 10.1 - Solve Prob. 10.30 assuming that force P is movedto...Ch. 10.1 - Two bars AD and DG are connected by a pin at Dand...Ch. 10.1 - Solve Prob. 10.32 assuming that the 900-N...Ch. 10.1 - Two 5-kg bars AB and BC are connected by a pin atB...Ch. 10.1 - A vertical force P with a magnitude of 150 N...Ch. 10.1 - Prob. 10.36PCh. 10.1 - 10.37 and 10.38 Knowing that the constant of...Ch. 10.1 - Prob. 10.38PCh. 10.1 - The lever AB is attached to the horizontal shaft...Ch. 10.1 - Solve Prob. 10.39, assuming that P = 350 N, l =250...Ch. 10.1 - Prob. 10.41PCh. 10.1 - The position of boom ABC is controlled by...Ch. 10.1 - The position of member ABC is controlled by the...Ch. 10.1 - The position of member ABC is controlled by...Ch. 10.1 - The telescoping arm ABC is used to provide...Ch. 10.1 - Solve Prob. 10.45, assuming that the workers...Ch. 10.1 - Denoting the coefficient of static friction...Ch. 10.1 - Knowing that the coefficient of static...Ch. 10.1 - A block with weight W is pulled up a plane forming...Ch. 10.1 - Derive an expression for the mechanical...Ch. 10.1 - Denoting the coefficient of static friction...Ch. 10.1 - Knowing that the coefficient of static...Ch. 10.1 - Using the method of virtual work,...Ch. 10.1 - Using the method of virtual work, determine...Ch. 10.1 - Referring to Prob. 10.43 and using the value...Ch. 10.1 - Prob. 10.56PCh. 10.1 - Prob. 10.57PCh. 10.1 - Prob. 10.58PCh. 10.2 - Using the method of Sec. 10.2C, solve Prob. 10.29....Ch. 10.2 - Using the method of Sec. 10.2C, solve Prob. 10.30....Ch. 10.2 - Using the method of Sec. 10.2C, solve Prob. 10.31....Ch. 10.2 - Using the method of Sec. 10.2C, solve Prob. 10.32....Ch. 10.2 - Using the method of Sec. 10.2C, solve Prob. 10.34....Ch. 10.2 - Prob. 10.64PCh. 10.2 - Using the method of Sec. 10.2C, solve Prob. 10.37....Ch. 10.2 - Prob. 10.66PCh. 10.2 - Prob. 10.67PCh. 10.2 - Show that equilibrium is neutral in Prob. 10.7....Ch. 10.2 - Two uniform rods, each with a mass m, areattached...Ch. 10.2 - Two uniform rods, AB and CD, are attached to gears...Ch. 10.2 - Two uniform rods AB and CD, of the same length...Ch. 10.2 - Two uniform rods, each of mass m and length l, are...Ch. 10.2 - Using the method of Sec. 10.2C, solve Prob....Ch. 10.2 - In Prob. 10.40, determine whether each of...Ch. 10.2 - A load W of magnitude 144 lb is applied to...Ch. 10.2 - Prob. 10.76PCh. 10.2 - Prob. 10.77PCh. 10.2 - Prob. 10.78PCh. 10.2 - A slender rod AB with a weight W is attached to...Ch. 10.2 - A slender rod AB with a weight W is attached totwo...Ch. 10.2 - Prob. 10.81PCh. 10.2 - A spring AB of constant k is attached to two...Ch. 10.2 - A slender rod AB is attached to two collars A and...Ch. 10.2 - Prob. 10.84PCh. 10.2 - 10.85 and 10.86 Cart B, which weighs 75 kN, rolls...Ch. 10.2 - 10.85 and 10.86 Cart B, which weighs 75 kN, rolls...Ch. 10.2 - 10.87 and 10.88 Collar A can slide freely on the...Ch. 10.2 - 10.87 and 10.88 Collar A can slide freely on the...Ch. 10.2 - Prob. 10.89PCh. 10.2 - A vertical bar AD is attached to two springs...Ch. 10.2 - Rod AB is attached to a hinge at A and to two...Ch. 10.2 - Rod AB is attached to a hinge at A and to...Ch. 10.2 - Two bars are attached to a single spring of...Ch. 10.2 - Prob. 10.94PCh. 10.2 - The horizontal bar BEH is connected to three...Ch. 10.2 - The horizontal bar BEH is connected to three...Ch. 10.2 - Bars AB and BC, each with a length l and of...Ch. 10.2 - Prob. 10.98PCh. 10.2 - Prob. 10.99PCh. 10.2 - Prob. 10.100PCh. 10 - Determine the vertical force P that must be...Ch. 10 - Determine the couple M that must be applied...Ch. 10 - Determine the force P required to maintain...Ch. 10 - Derive an expression for the magnitude of the...Ch. 10 - Derive an expression for the magnitude of the...Ch. 10 - A vertical load W is applied to the linkage at B....Ch. 10 - A force P with a magnitude of 240 N is applied to...Ch. 10 - Two identical rods ABC and DBE are connected bya...Ch. 10 - Solve Prob. 10.108 assuming that the 24-lb load...Ch. 10 - Two uniform rods each with a mass m and length...Ch. 10 - A homogeneous hemisphere with a radius r isplaced...Ch. 10 - A homogeneous hemisphere with a radius r isplaced...
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