# Online Engineering Mechanics Test - Engineering Mechanics Test 3

Instruction:

• This is a FREE online test. DO NOT pay money to anyone to attend this test.
• Total number of questions : 20.
• Time alloted : 30 minutes.
• Each question carry 1 mark, no negative marks.
• DO NOT refresh the page.
• All the best :-).

1.

Determine the angle :

A.
 = 30°
B.
 = 40°
C.
 = 60°
D.
 = 50°

2.

The cord is attached between two walls. If it is 8 m long, determine the distance x to the point of attachment at B.

A.
 x = 7.75 m
B.
 x = 7.68 m
C.
 x = 6.93 m
D.
 x = 7.94 m

3.

The cable AO exerts a force on the top of the pole of F = {—120i — 90j — 80k} lb. If the cable has a length of 34 ft, determine the height z of the pole and the location (x,y) of its base.

A.
 x = 16 ft, y = 16 ft, z = 25 ft
B.
 x = 12 ft, y = 9 ft, z = 8 ft
C.
 x = 20 ft, y = 10 ft, z = 14 ft
D.
 x = 24 ft, y = 18 ft, z = 16 ft

4.

What is the projection of the force F2 along the positive axis?

A.
 F2y = 170.0 N
B.
 F2y = —80.0 N
C.
 F2y = 90.0 N
D.
 F2y = 120.0 N

5.

Determine the magnitude and direction of the resultant force.

A.
 R = 251 N, = 85.5° CCW
B.
 R = 251 N, = 94.5° CCW
C.
 R = 421 N, = 67.7° CCW
D.
 R = 421 N, = 112.3° CCW

6.

Determine the design angle ( <90°) bretween the two struts so that the 500-lb horizontal force has a component of 600lb directed from A toward C. That is the component of force acting along member AB?

A.
 FAB = 321 lb, = 40.0°
B.
 FAB = 383 lb, = 36.9°
C.
 FAB = 171.1 lb, = 20.0°
D.
 FAB = 215 lb, = 52.7°

7.

Replace the force at A by an equivalent force and couple moment at P.

A.
 F = 15 kN @ = 36.9° , Mp = 67.1 kN-m
B.
 F = 15 kN @ = 36.9° , Mp = 30 kN-m
C.
 F = 15 kN @ = 143.1° , Mp = 67.1 kN-m
D.
 F = 15 kN @ = 143.1° , Mp = 30 kN-m

8.

Replace the force and couple system by an equivalent single force and couple acting at point P.

A.
 F = (-0.0858i-1.184j) kN, M = 36.6 kN-m
B.
 F = (-0.0858i-1.184j) kN, M = 21.6 kN-m
C.
 F = (-0.0858i-1.184j) kN, M = 13.61 kN-m
D.
 F = (-0.0858i-1.184j) kN, M = 35.7 kN-m

9.

The three forces acting on the water tank represent the effect of the wind. Replace this system by a single resultant force and specify its vertical location from point O.

A.
 R = 600 lb, d = 65.0 ft below O
B.
 R = 600 lb, d = 130.4 ft below O
C.
 R = 600 lb, d = 65.0 ft above O
D.
 R = 600 lb, d = 130.4 ft above O

10.

Compute the horizontal and vertical components of force at pin B. The belt is subjected to a tension of T=100 N and passes over each of the three pulleys.

A.
 Bx = 0 N, By = 141.4 N
B.
 Bx = -15.89 N, By = 120.7 N
C.
 Bx = 20.7 N, By = 157.3 N
D.
 Bx = 0, By = 100.0 N

11.

A tower used in an electrical substation supports a power line which exerts a horizontal tension of T = 500 lb on each side truss of the tower as shown. Determine the force in members BC, CM, and LM of a side truss and indicate whether the members are in tension or compression.

A.
 CM = 833 lb T, CB = 3330 lb C, LM = 2670 lb T
B.
 CM = 581 lb T, CB = 2050 lb C, LM = 2000 lb T
C.
 CM = 325 lb T, CB = 3040 lb C, LM = 2670 lb T
D.
 CM = 58 lb T, CB = 1646 lb C, LM = 1600 lb T

12.

Determine the approximate amount of paint needed to cover the surface of the water storage tank. Assume that a liter of paint covers 2.5 m2. Also, what is the total inside volume of the tank.

A.
 27.6 liters of paint, V = 52.6 m3
B.
 20.1 liters of paint, V = 50.3 m3
C.
 26.4 liters of paint, V = 56.5 m3
D.
 25.1 liters of paint, V = 55.0 m3

13.

A package is dropped from the plane which is flying with a constant horizontal velocity of vA = 150 ft/s at a height h = 1500 ft. Determine the radius of curvature of the path of the package just after it is released from plane at A.

A.
 2 = 9860 ft
B.
 2 = 3000 ft
C.
 2 = 1500 ft
D.
 2 = 8510 ft

14.

As the instant shown, cars A and B are traveling at speeds of 20 mi/h and 45 mi/h, respectively. If B is acceleration at 1600 mi/h2 while A maintains a constant speed, determine the magnitudes of the velocity and acceleration of A with respect to B.

A.
 vA/B = 33.9 mi/h, aA/B = 1600 mi/h2
B.
 vA/B = 60.8 mi/h, aA/B = 1600 mi/h2
C.
 vA/B = 33.9 mi/h, aA/B = 1426 mi/h2
D.
 vA/B = 60.8 mi/h, aA/B = 1426 mi/h2

15.

The firing mechanism of a pinball machine consists of a plunger P having a mass of 0.25 kg and a spring of stiffness k = 300 N/m. When s = 0, the spring is compressed 50 mm. If the arm is pulled back such that s = 100 mm and released, determine the speed of the 0.3 kg pinball B just before the plunger strikes the stop, i.e., s = 0. Assume all sufaces of contact to be smooth. The ball moves in the horizontal plane. Note that the ball slides without rolling.

A.
 v = 4.47 m/s
B.
 v = 3.30 m/s
C.
 v = 2.34 m/s
D.
 v = 3.16 m/s

16.

A golf ball having a mass of 40 g is struck such that it has an initial velocity of 200 m/s as shown. Determine the horizontal and vertical components of the impulse given to the ball.

A.
 Impx = 4.00 N-s, Impy = 6.93 N-s
B.
 Impx = 6.93 N-s, Impy = 4.00 N-s
C.
 Impx = 6.93 N-s, Impy = 4.39 N-s
D.
 Impx = 4.00 N-s, Impy = 7.32 N-s

17.

A basket and its contents weigh 10 lb. A 20-lb monkey grabs the other end of the rope and very quickly (almost instantaneously) accelerates by pulling hard on the rope until he is moving with a constant speed of vm/r = 2 ft/s measured relative to the rope. The monkey then continues climbing at this constant rate relative to the rope for 3 seconds. How fast is the basket rising at the end of the 3 seconds? Neglect the mass of the pulley and the rope.

A.
B.
C.
D.

18.

The motor M pulls on the cables with a force F that has a magnitude which varies as shown on the graph. If the 15-kg crate is originally resting on the floor such that the cable tension is zero when the motor is turned on, determine the speed of the crate when t = 6s.

A.
 vcrate = 23.2 m/s
B.
 vcrate = 70.0 m/s
C.
 vcrate = 11.14 m/s
D.
 vcrate = 58.0 m/s

19.

A hockey puck is traveling to the left with a velocity of v1 = 10 m/s when it is struck by a hockey stick and given a velocity of v2 = 20 m/s as shown. Determine the magnitude of the net impulse exerted by the hockey stick on the puck. The puck has a mass of 0.2 kg.

A.
 Imp = 6.00 N-s
B.
 Imp = 2.00 N-s
C.
 Imp = 2.78 N-s
D.
 Imp = 5.68 N-s

20.

THe 500-g rod AB rests along the smooth inner surface of a hemispherical bowl. If the rod is released from the position shown, determine its angular velocity at the instant it swings downward and becomes horizontal.

A.
B.
C.
D.