The uniform smooth rod in Example 5.10 is supported by a smooth wall at A and rollers at B and C. The reactions at B and C are found to be By = -1 kN and Cy = 1.35 kN, and they act at 30 degrees from the vertical. What is the reaction at the smooth wall, Ax?

Correct answer: 173 N

Explanation

This question demonstrates solving for a final unknown reaction after other reactions have been determined, paying close attention to the signs. The negative value for By indicates its direction is opposite to the one assumed in the FBD, and this must be carried through in subsequent calculations.

Other questions

Question 1

What are the two fundamental conditions required for a rigid body to be in equilibrium?

Question 2

In a two-dimensional analysis, what type and number of unknown reactions does a smooth pin or hinge support provide?

Question 3

What is the primary purpose of drawing a free-body diagram (FBD) in mechanics?

Question 4

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Question 5

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Question 6

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Question 8

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Question 9

Why are internal forces not included on the free-body diagram of an entire rigid body?

Question 10

What does a negative scalar result for an unknown force in an equilibrium calculation signify?

Question 11

The foot lever in Example 5.2 is subjected to a vertical force F from an operator's shoe. The spring is stretched 1.5 in. and has a stiffness k = 20 lb/in. What is the horizontal force exerted by the spring on the lever?

Question 12

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Question 13

Which of the following is an example of an improperly constrained 3D system?

Question 14

For the box wrench in Example 5.8, a moment MA and force components Ax and Ay are exerted on the wrench at the bolt A. The wrench is subjected to a 30 N force at 60 degrees and a 52 N force with a 5-12-13 slope. What is the value of the vertical force component Ay at A?

Question 15

A cord wrapping over a frictionless pulley supports a 100 lb force. What is the tension T in the cord on the other side of the pulley?

Question 16

What are the three equations in the standard set of equilibrium equations for a 2D coplanar force system?

Question 17

A member is pin-connected at A and rests against a smooth support at B. The reaction force NB at the smooth support is 200 N, directed at 30 degrees to the vertical. What is the horizontal component of the reaction at pin A (Ax)?

Question 18

In a 3D system, how many scalar equations of equilibrium are available for a single rigid body?

Question 20

What type of support reaction is provided by a cable?

Question 21

A uniform truck ramp with a weight of 400 lb is held in position by two side cables. The ramp is 10 ft long, held at a 30-degree angle, and its center of gravity is at the midpoint. What is the total tension T in the two cables combined, calculated by summing moments about the pin support A?

Question 22

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Question 23

In a 2D system, what reaction does a roller support provide?

Question 24

The lever ABC in Example 5.13 is a three-force member. The lines of action of the 400 N force and the force F from link BD (at 45 degrees) are known. If these forces must be concurrent at point O for equilibrium, and the horizontal distance from A to the line of action of the 400 N force is 0.5 m, what is the angle θ of the reaction force FA at pin A?

Question 25

In a 3D system, what type and number of unknown reactions does a single fixed support provide?

Question 26

A homogeneous plate with a mass of 100 kg is supported by a roller at A, a ball-and-socket at B, and a cord at C. The plate has dimensions of 3m by 2m. A 300 N force is applied parallel to the 3m side, and a 200 N·m couple moment is applied. Given the weight is 981 N, what is the magnitude of the reaction at the roller A?

Question 27

What is the key difference in the free-body diagram of a single pipe versus the FBD of two pipes in contact combined as a single system?

Question 28

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Question 29

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Question 30

For the rod AB shown in Fig. 5-31a, supported by a ball-and-socket at A and two cables BD and BE, what is the reaction component Az at A if a 200 N force is applied vertically at joint C?

Question 31

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Question 32

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Question 33

In a 2D system, what reaction does a member pin-connected to a collar on a smooth rod provide?

Question 34

If a body is supported by a single journal bearing with a square shaft in a 3D system, how many unknown reactions are there?

Question 35

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Question 36

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Question 37

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Question 38

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Question 39

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Question 40

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Question 41

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Question 42

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Question 43

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Question 44

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Question 45

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Question 46

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Question 47

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Question 48

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Question 49

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Question 50

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