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# Prol assignment.doc - Bowmanville High School

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Prol assignment.doc - Bowmanville High School

Torque and Equilibrium Practice Problems

Trusses and Frames

1. A simple roof truss is composed of two rafters and a horizontal tie, held together by one single pin at each vertex. If a 100kg mass is hung from the apex of the rafters, as illustrated, what is

a) the additional compression in each rafter,

b) the additional tension in the tie, and

c) the additional compression in each stud? 332(1.3 x 10 N, 1.2 x 10 N, 4.9 x 10 N)

Torque

2. Calculate the torque of each force about the corresponding point P. (75 Nm, 26 Nm, 13 Nm, )

3. A uniform, 12.0 m long girder has a mass of 500 kg. It rests, unattached, on a concrete slab overhanging the

edge by 5.5 m. How far can an 80 kg man walk out on the girder before it tips? (3.1 m)

4. A short-wave aerial is attached to the top of a mast 20m high, and exerts a force of 600 N on the top of the

mast (see diagram). The mast is supported by a guy wire running to the ground from a point of 6.0m below

the top of the mast, inclined 60 degrees to the horizontal. The mast is pivoted on a hinge pin at its base. 3Determine the tension of the guy wire and the reaction forces exerted on the mast by the ground. (1.7 x 10 N)

Question 4 Question 5 600 N

5. A 41 kg trap door, 1.2 m long, is supported by a hinge at A and a sloping rope at B. Find the tension in the

rope and the vertical and horizontal reactions of the hinge if the rope is just about to open the trap door. 22 (2.2 x 10 N, 93 N, 2.0 x 10 N)

6. A 40 kg plank, 6.0 m long, is supported by sawhorses A and B, as shown. A 60kg crate is placed on the plank, 22222.0 m from B. [a) 3.9 x 10 N, 5.9 x 10 N; b) 3.3 x 10 N, 6.5 x 10 N]

a) Find the reaction forces at A and B. b) Find the reaction forces at A and B.

7. A 3.0 m diving board with a mass of 26 kg is fastened securely at two points A and B, as illustrated. If a 46kg 23diver stands 0.50 m from the end, find the forces A and B. (8.0 x 10 N [down], 1.5 x 10 N [Up])

8. A 6.0 m ladder with a mass of 12.5 kg leans against a smooth wall at an angle of 50; to the horizontal. If the

coefficient of static friction between the ladder and the ground is 0.40, how far up the ladder can a 70 kg

woman climb before the ladder starts to slip? (3.2 m from the top)

9. A 12 kg plank has four concrete blocks placed on it, as illustrated. If each block has a mass of 10 kg and a

width of 24 cm, where is the center of gravity of the system, located from the left end? See next page for

diagram.

Question 9 Diagram Question 10 Diagram

10. The center of gravity of a person may be located by the arrangement shown in the diagram. Assuming the

scales to be adjusted to zero with the plank alone, locate the center of gravity of the person. (1.2 m) 11. A cylindrical steel rod of radius 2.0 cm and length 40 cm is turned down on a lathe to one-half of it’s radius

for a distance of 30 cm from one end. Find the center of gravity, measured from the thicker end. 3(density of steel = 7.89 X 10 kg/m) (0.14 m)

12. A triangular steel sheet, with equal sides of 10 cm, is pushed at its peak. If the triangle is pushed parallel to

its base, what angle will the base of the triangle make when it just begins to tip over? 13. A transport truck 4.3 m tall and 2.4 m wide has a center of mass 2.5 m high along the midline. How steep a

slope can the truck be parked on without tipping over sideways? 514. A marble column supporting a load of 1.0 X 10 kg has a diameter of 0.5 m. 62a. What is the stress in the column? (5.0 x 10 N/m) -4b. What is the strain in the column? (1.0 x 10) -3c. If the column is 12 m high, how much will it be compressed? (1.2 x10 m)

15. An aluminum wire 1.0 m long is elongated to 0.02 cm when under stress. If a brass wire with an identical

diameter were used to support the same load, what would its initial length have been for it to have had the

same extension? (1.3 m)

16. How much will a 40 m steel elevator cable stretch if its diameter is 2.0 cm and it is supporting a static load of 4-31.5 X 10 N? (9.6 x 10 m)

17. A 50 cm long rod with a diameter of 1.0 cm is used to support a load of 100 N along its length. As a result, -3the rod is compressed 9.1 X 10 mm. What is the Young’s Modulus of the rod? What is the material? -4218. A rectangular steel column 2.5 m long, with a cross sectional area of 2.7 X 10 m is used vertically to 3-support a sagging floor. If the column supports a load of 5.5 X 10 kg, how much is it compressed? (2.5 x 103 m)

19. A steel cable supports a 3000 kg elevator. Allowing for a safety factor of 4,

calculate the diameter of the cable required if the maximum acceleration is 2-2 1.0 m/s. (1.8 x 10 m)

20. Given the dimensions on the diagram of the forearm holding a mass of 5.4 kg, find 2a. the tension in the biceps muscle and (4.4 x 10 N) 2b. the reactive force of the radius on the humerus, at the joint. (3.8 x 10 N)

21. A ballerina holds her 3.9 kg arm out horizontally such that her arm’s centre of mass is 34 cm from her

shoulder joint. Her deltoid muscle is attached to her arm 14 cm from the joint and pulls her arm upward 17;

above the horizontal.

a. What is the tension in the deltoid muscle? (317 N [left 17; up]) b. answer = 310 N [down 80; right]

b. What is the reaction force (magnitude and direction) of her shoulder on her humerous (arm bone)?

Elastic Moduli of Various Substances Ultimate Strengths of Various Materials (Force/Area)

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