1. Please complete the following short problems.

Size: px

Start display at page:

Download "1. Please complete the following short problems."

Mary French
5 years ago
Views:

1 Name 1. Please complete the following short problems. For parts 1A and 1B, we will consider three M88 recovery vehicles pulling an M1 tank back onto the road as shown below. F2 F1 50 M88 #1 50 M88 #2 y A x M88 #3 B A M1 tank F3 B 12 ft G 20 ft 1A. If the magnitude of the cable forces acting on the tank are known to be F1 = 10,000 lb, F2 = 15,000 lb and F3 = 20,000 lb, determine the total moment that the cable forces F 1, F 2 and F 3 exert about the tank s center of mass (see figure of tank above right). Assume that the tank s center of mass G is at the geometric center of the rectangle shown. (6 points) M G =

2 Name 1B. What is the total resultant force due to all three forces acting on the tank? Please write your answer in vector form. (4 points) F total = 1C. Determine the component of the moment about the x axis generated by the two wrenches. (4 points) Mx =

3 Name 1D. What is the projection of the force in cable CD in the direction of the line connecting points O and F? (6 points) FOF =

4 Name 2. A seat/harness combination shown is required to carry an 800 N load. 2A. First, draw a free body diagram in the space provided. (6 points) 2B. Second, find the unit vectors that provide the directions for the forces in cables AD, BD, and CD. (6 points) u AD = u BD = u CD =

5 Name 2C. If the system is in equilibrium, determine the magnitude of the tensile force in each cable. (8 points) T AD = T BD = T CD =

6 Name 3A. A catwalk with a mass of 100 kg has two roller supports and a cable fastening it to the dock. In the space provided, please draw a complete free body diagram. (5 points) Free Body Diagram Determine the magnitudes of the forces at A and B as well as the tension, T, in the cable. (6 points)

7 Name 3B. Determine the total force due to each distributed load. Then, on a separate figure, replace the distributed load with a single concentrated force at the correct location. Recall that x = x 1/2. (5 points) Replace the distributed load with a single force here. Total Force = Location =

11 ME Fall 2004 Examination No. 1 PROBLEM NO. 1 Given: Force-couple system I shown below left is made up of four forces F 1, F 2, F 3 and F acting at points A, B, C and D, respectively, in addition to a couple M. Force F and couple M are known to have magnitudes of 200 lb and 900 ft-lb, respectively. Force-couple system II shown below right is made up of a force R at B and a couple M B, with R and M B, having known magnitudes of 300 lb and 600 ft-lb, respectively. Find: If System II is to be the equivalent force-couple of System I, what are the magnitudes of the forces F 1, F 2 and F 3? A F 1 A F 3 R 2ft M = 900 ft-lb C equivalent C B 4ft 2ft y B M B F 2 F = 200lb D x D

12 ME Fall 2004 Examination No. 1 PROBLEM NO. 2 Given: Find: Pole OE is supported by a ball-and-socket joint at O and cables AC and BE. A downward vertical force F acts at end E. Consider the weight of the pole to be negligible and the ball-and-socket joint at D to be frictionless. a) Complete the free body diagram of the pole given below right. b) Resolve the forces of cables AC and BE on the pole in terms of their unknown magnitudes and known unit vectors. c) If F = 1000 lb, find the tension in cables AC and BE. z 3 ft B A 3 ft 2 ft 2 ft O 1.5 ft C 1.5 ft E y F x

13 Name (Print) (Last) (First) ME Fall 2005 Exam 1 PROBLEM NO. 1 1A. If the PCI card weighs 0.8 lb. and the weight acts at the point indicated, calculate the moment it exerts about the origin (O). Write it in vector form. (0 or 4 points)

14 Name (Print) (Last) (First) 1B. The coordinates of point A are (x = m, y = m, and z = m). Express the force that the rope AB exerts on the frictionless slider in vector form if the tension in the rope, T AB = 357 N. (0 or 4 points). z y x

15 Name (Print) (Last) (First) 1C. The positions of the Sun, Mercury, Earth, and Venus are known at a particular instant. The approximate distance from the Sun to Mercury is 57x10 6 km, from the Sun to Venus is 108x10 6 km, and the distance from the Sun to the Earth is 150x10 6 km. Assuming that all the planets and the Sun lie in the x-y plane, θ = 20 o, and φ = 40 o, calculate the unit vector from Mercury to Earth. (0 or 4 points)

16 Name (Print) (Last) (First) 1D. Calculate the equivalent forces and moments at point A if F D = 800 N. (0 or 4 points).

17 Name (Print) (Last) (First) 1E. A team of engineers is designing a hull for a new racing yacht and they want to determine the drag force exerted on the boat when water is moving past at a known velocity. To do so, a model of the proposed hull is placed in a test channel. Dynamometer readings indicate that the tension in cable AB, T AB, is 40 lb. and cable AE experiences a force of 60 lb. What is the component of T AB, in the direction of AE? (0 or 4 points).

18 Name (Print) (Last) (First) ME Fall 2005 Exam 1 PROBLEM NO. 2 Poles AB and EF are each 22 m tall and support a circus high wire. They are each held in their vertical positions by guy wires. The tension acting in the high wire suspended between the poles is 9 kn. Assume the weight of the wires can be neglected. The weight of each pole is 1 kn. Draw a complete free body diagram of pole AB, assuming that the point A is a ball-and-socket joint. Find the forces acting on guy wires BC and BD. (20 points).

19 Name 2. The tree below has been secured by cables stretching from A to points B, C, and D, respectively. The base of the tree is located at (0, 0, 0) m. 2a. If the force in cable AD is 1,560 N, write out the force in vector form (4 points). F AD =

20 Name 3. The semi-circular plate has a radius of 40 cm. The plate weighs 100 N with the center of gravity at (d, 0, 0). 3a. First, draw a free body diagram of the semi-circular plate, assuming the connection at C is a ball-and-socket joint (6 points).

Name ME 270 Summer 2005 Examination No. 1 PROBLEM NO. 1 Given: The net wind force, F = Fu, acting on the sail of the Team USA racing boat has a magnitude of 950 N. The unit vector, u = mxi + 0.52j 0.

21 Name ME 270 Summer 2005 Examination No. 1 PROBLEM NO. 1 Given: The net wind force, F = Fu, acting on the sail of the Team USA racing boat has a magnitude of 950 N. The unit vector, u = mxi j 0.08k. The coordinates of the points A (the base of the mast), B (the point at which F is applied), and C (the top of the mast) at this instant are measured relative to the coordinate system shown: A (-32 m, 4m, 0m) B (-32.4m, 6.7m, 12m) C(-33.4m, 5.9m, 21m) Find: Write out the components of the vector, F. Calculate the moment that F exerts about the base of the mast. What is the scalar component of F in the direction of the mast?

22 Name ME 270 Summer 2005 Examination No. 1 PROBLEM NO. 2 Given: The plane shown below is set up on a test stand with only one engine running. These systems are able to use the force sensors at A, B, and C to determine the engine s thrust in situ. It should be noted that the engine not only exerts a thrust, T, but it generates a torque, Q, as well. Stands A and B can exert (and measure) forces in all three directions while the stand at C can exert (and measure) a force only in the vertical direction. The magnitude of T is 5,000 lbs. and the magnitude of Q is 1250 ft.*lbs., and the plane weighs 22,300 lbs. We should also note that L = 20 ft., h = 6 ft., a = 8 ft., and b = 12 ft. Find: Assume that the stands are strong enough to maintain static equilibrium for the plane and: a) Complete the free body diagram of the plane on the next page. b) For the given forces and dimensions, calculate the vertical component of the forces at A, B, and C.

23 Name

Engineering Mechanics: Statics in SI Units, 12e

Engineering Mechanics: Statics in SI Units, 12e 5 Equilibrium of a Rigid Body Chapter Objectives Develop the equations of equilibrium for a rigid body Concept of the free-body diagram for a rigid body