Problem Set

1

1.1. Determine the magnitude of the

resultant force and its direction, measured

counter-clockwise from the positive x-axis.

Ans: R = 998 N, θ = 135°

1.2. Two forces are applied at the end of a

screw eye in order to remove the post.

Determine the angle θ (0° ≤ θ ≤ 90°) and

the magnitude of the force F so that the

resultant force acting on the post is directed

vertically upward and has a magnitude of

750 N.

Ans: θ = 18.6°, F = 319 N

1.3. Determine the magnitude and

direction of F1 so that particle P is in

equilibrium.

Ans: θ = 12.9°, F1 = 552 N

Problem Set 2

2.1 Determine the angle θ between the

tails of the two vectors.

Ans: θ = 121°

2.2 Determine the magnitude and

directional sense of the resultant

moment of the forces about point P.

Ans: MP = 3.15 kN-m ccw

2.3 Determine the magnitude and

directional sense of the moment of the

force at A about point P.

Ans: MP = 3.15 kN-m ccw

2.4 Determine the moment of the force

at A about point O. Express the result

as a Cartesian vector.

Ans: MO = (260i + 180j + 510k)N-m

Problem Set 3

3.1 Determine the horizontal and

vertical components of reaction for the

beam loaded as shown. Neglect the

weight of the beam.

Ans:

Ay = 319 N, Bx = 424 N, By = 405 N

3.2 The lever ABC is pin-supported at

A and connected to a short link BD as

shown. If the weight of the members is

negligible, determine the components

of the force of the pin on the lever at A.

Ans: Ax = 533 N, Ay = 933 N

3.3 If the wheelbarrow and its contents

have a mass of 60 kg and a center of

mass at G, determine the magnitude of

the resultant force which the man must

exert on each of the two handles in

order to hold the wheelbarrow in

equilibrium.

Ans: FB = 105 N

3.4 Determine the distance d for

placement of the load P for equilibrium

of the smooth bar in the position θ as

shown. Neglect the weight of the bar.

Ans: d = a/cos3θ

Problem Set 4

4.1 Determine the force in each

member of the truss and state if the

members are in tension or compression.

Assume each joint as a pin.

Let P = 4 kN

Ans:

FAE = 8.94 kN (C), FAB = 8.00 kN (T),

FBC = 8.00 kN (T), FBE = 8.00 kN (C),

FCE = 8.94 kN (T), FDE = 17.9 kN (C)

4.2 Determine the force in members

BC, CH and GH of the bridge truss, and

indicate whether the members are in

tension or compression.

Ans:

FGH = 29.0 kN (C), FBC = 20.5 kN (T),

FCH = 12.0 kN (T)

4.3 Determine the force in members

CD, CF and FG of the Warren truss,

and indicate whether the members are

in tension or compression.

Ans:

FFG = 8.08 kN (T), FCD = 8.47 kN (C),

FCF = 0.770 kN (T)

Problem Set 5

5.1 The engine hoist is used to support

the 200-kg engine. Determine the force

acting in the hydraulic cylinder AB, the

horizontal and vertical components of

force at the pin C and the reactions at

the fixed support D.

Ans:

FAB = 9.23 kN

Cx = 2.17 kN

Cy = 7.01 kN

Dx = 0

Dy = 1.96 kN

MD = 2.66 kN-m

5.2 The compound arrangement of the

pan scale is shown. If the mass on the

pan is 4 kg, determine the horizontal

and vertical components of force at pins

A, B and C and the distance x of the

25-g mass to keep the scale in balance.

Ans:

Ay = 34.0 N, Ax = 0

Cy = 6.54 N, Cx = 0

By = 1.06 N, Bx = 0

x = 292 mm,

Problem Set 6

6.1 The coefficient of friction between

the shoes at A and B of the tongs and

the pallet is μ’s= 0.5, and between the

pallet and the floor is μs= 0.4. If a

horizontal towing force P = 300 N is

applied to the tongs, determine the

largest mass that can be towed.

Ans: m = 54.9 kg

6.2 A cylinder having a mass of 250 kg

is to be supported by the cord which

wraps over the pipe shown. Determine

the largest vertical force F that can be

applied to the cord without moving the

cylinder if the rope passes over the pipe

(a) once or (b) twice. Let μs= 0.2.

Ans:

(a) F = 4.60 kN

(b) F = 16.2 kN

6.3 Blocks A and B have mass of 7 kg

and 10 kg, respectively. Using the

coefficients of static friction shown,

determine the largest vertical force P

which can be applied to the cord

without causing motion.

Ans: P = 223 N