Statics Of Rigid Bodies 655x6e

1. Determine the resultant of the four parallel forces acting on the rocker arm. 320 N

150 N

280 N

3. Replace the distributed loading by an equivalent resultant force and specify its location on the beam, measured from the pin at A.

350 N 4 kN/m

O

A

B

2m

2m

2. Determine the resultant of the for system shown and specify its point of application, measured along the x-axis from point O.

4. Replace the loading on the beam by an equivalent resultant force and specify its location measure from point A. 2.5 kN/m 1.5 kN/m 0.5 kN/m

A B 3m

1m

1. Determine the resultant of the four forces and one couple that act on the plate shown. 2m 70 N

5m

Y

50 N

45 150 Nm

2m

90 N

2m O

X

50 N

1m

3. The Howe roof truss shown carries the given loads. The wind loads are perpendicular to the inclined . Determine the magnitude of the resultant, its inclination with the horizontal, and where it intersects AB. 1250 lb 2500 lb

1250 lb

2250 lb 10'

A 10'

3250 lb

2. Determine completely the resultant (magnitude, direction and position) of the system of forces shown. Each force make an angle of 15⁰ with the vertical. 1 kN

A

2 kN

3 kN

1.5 kN

B

10'

10'

10' 2250 lb

1250 lb

4. Determine the resultant R of the three forces acting on the simple truss. Specify the points on the x and y axes through which R must . 20 kN

30

25 kN 5m

Y O

6m

3m

3m

X

30 kN

6. Replace the force and couple system acting on the frame by an equivalent resultant force and specify where the resultant’s line of action intersects member BC, measured from B. A 2'

4 3 500 lbf t

C 50 lb

5. Calculate the y-coordinate of the point on the y-axis through which the resultant of the three forces and couple must . 60 Nm

100 N

200 mm

100 N

Y 30 300 mm

O 600 N

400 mm 100 N

4'

150 lb

3'

B

1. Determine the magnitude of F and the orientation ɵ of the 750-N force so that the particle is in equilibrium. Y 450 N

F 

700 N

3. Determine the values of the angles α and θ so that the forces will be in equilibrium.

15

X

80 lb

750 N

 

150 lb

110 lb

2. Determine the magnitude F1 and F2 so that the particle at the origin O is in equilibrium. Y F1

500 N

O

45

X

30

4. If the value P is 280 lb, determine the angle θ at which it must be inclined with the smooth plane hold the 500-lb box in equilibrium. W = 500 lb

F2

P



30

6. Determine the tension in each cable to maintain the position in equilibrium if box D weighs 60 N and box E weighs 80 N. A

45

B D

E

5. Determine all the cable tensions and the mass of block E of the system shown below. Use the vector triangle method. A D 40

B 20

C

50 kg E

60

C

1. Determine the reactions of the beam loaded as shown. The uniformly distributed load is 200 lb/ft. Neglect the weight of the beam.

3. Determine the reactions R1 and R2 of the beam loaded with a concentrated load of 1500 lb and a load varying from zero to an intensity of 500 lb per ft. 500 lb/ft

200 lb/ft

1500 lb

5' 12'

R2

R1

3'

1'

12'

R1

R2

2. The beam shown is built into a wall so that it rests against points A. The beam is 6m long and has a mass of 100 kg. Compute the reaction and moment at A. 1200 N

A

2m

2m

200 N/m

4. The wheel lads are given as shown. Determine the distance x so that the reaction of the beam at A is twice as great as the reaction at B. 750 lb 300 lb x

4'

A

B

15'

4. The roof of truss is ed by a hinge at A and a roller at B. Determine the values of reactions. 700 N

700 N

700 N

500 N

A

500 N

30

30

5m

5m 1500 N

5m 1000 N

B

1. Determine the reactions at A and B if α = 30⁰. 50 lb

2. The frame shown s part of the roof of a small building. Knowing that the tension in the cable is 180 kN, determine the reaction at the fixed end E. D

6'

6' 2.25m A



B C 1.8 m

1.8 m

1.8 m

1.8 m

8' 20 kN

20 kN

20 kN

20 kN

3.75m





E

4.5m

3. A light bar AB s a 15-kg at its midpoint C. 4. Determine the horizontal and vertical components Rollers at A and B rest against frictionless surfaces, and of reaction for the beam loaded as shown. Neglect the a horizontal cable AD is attached at A. Determine the weight of the beam. 300 N 700 N tension in cable AD and the reactions at A and B. 250mm

250mm

15 kg

45

B A

B 2m

3m

C

C 350mm 200 N

A

D

2m

5. Determine the reactions (forces) at the roller at A and the pin at B.

6. While slowly walking, a man having a total mass of 80 kg places all his weight on one foot. Assuming that the normal force Nc of the ground acts on his foot at C, determine the resultant vertical compressive force FB which the tibia T exerts on the astragalus B, and the vertical tension FA in the Achilles tendon A at the instant shown.

1. Determine the force P for impending motion up the plane of the 85-lb block shown in the figure. The coefficient of friction is 0.30. 5

P

12

3.The coefficients of friction are µs = 0.25 and µk = 0.2 between all surfaces in for the given figure. Knowing that P = 90 N, determine (a) the resultant of the frictional forces exerted on block B if block A is restrained as shown (b) the frictional forces exerted by the ground on block B if the cable is removed.

A 10kg B 15kg

P

2. The coefficient of friction between the block and the incline is µs = 0.30 and µx = 0.25. Determine whether the block is in equilibrium and find the magnitude and direction of frictional force when ɵ = 20⁰ and P = 1kN. 1.5 kN

P 

4. The coefficients of friction between the 50 kg block and the incline are µs = 0.35 and µx = 0.3. Determine whether the block is in equilibrium and find the magnitude and direction of frictional force when FP = 1kN directed towards the block. FP kg 50

45



6. A packing crate of mass 40 kg must be moved to the left along the floor without tipping. Knowing that the coefficient of static friction is between the crate and the floor is 0.3, determine (a) the largest allowable value of α, (b) the corresponding magnitude of force P P (c) the frictional force. 

5. Block A weighs 10 kg and block B weighs 5 kg. Knowing that the angle of friction for all surface in is 10⁰, and that there is no frictional force between the blocks and the incline, determine the angle θ for which the motion is impending.

A B



0.75 m

1m