Equilibrium of a Rigid Body

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

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

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

What defines a two-force member?

What conditions must the forces on a three-force member satisfy for it to be in equilibrium?

In a 2D system, a beam is supported by a rocker at A and a pin at B, 7 m away. A vertical 100 N force is applied 5 m from A, and a vertical 200 N force is applied at A. What is the vertical reaction at the pin B (By) if you check the result by summing moments about point A?

A system is described as 'statically indeterminate' when...

In a three-dimensional system, how many unknown reactions can a single ball-and-socket joint provide?

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

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

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?

A uniform beam has a mass of 100 kg. What is the magnitude of the weight of the beam that should be included on its free-body diagram?

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

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?

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?

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

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)?

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

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?

What type of support reaction is provided by a cable?

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?

A collar at A is fixed to a member and can slide vertically along a shaft. A 900 N force acts horizontally at 1.5 m from the shaft and another 900 N force acts vertically at the end of the member, 3 m + (1 m)cos(45) from the shaft. What is the reaction moment MA exerted by the collar on the member?

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

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?

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

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?

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?

A rod assembly is supported by a ball-and-socket joint at A, a smooth journal bearing at B, and a roller at C. A 900 N force is applied vertically. What is the reaction force at the roller C?

When is it appropriate to model a physical connection as a 'weightless link'?

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?

Under what condition can an alternative set of 2D equilibrium equations, ΣFx = 0, ΣMA = 0, and ΣMB = 0, be used?

A bent rod is supported by a journal bearing at A and a ball-and-socket at D. A cable BC holds it in equilibrium against a 100 kg weight. The tension in the cable BC (TB) is found to be 490.5 N. If one sums moments about the axis DA, what is the value of the moment produced by the 981 N weight acting at E, given rE = -0.5j?

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

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

The weight of a body is considered what type of force in a free-body diagram?

In the 'Procedure for Analysis' for 2D equilibrium, why is it suggested to apply the moment equation about a point that lies at the intersection of the lines of action of two unknown forces?

A pin at A exerts force components Ax and Ay on a lever. A link at B exerts a 20 lb force at an angle. A spring exerts a 30 lb horizontal force. An operator applies a vertical force F. The dimensions are 5 in from A to the spring and link, and 8 in from A to the force F. If the system is in equilibrium, what equation results from summing moments about A?

In a 3D system, a single journal bearing can resist which of the following?

A boom is supported by a pin at A and a cable BC. The boom has a weight of 650 lb at G and supports a load of 1250 lb at B. To solve for the reactions at pin A and the tension in cable BC, what is the first step?

A bar rests on three smooth points of contact A, B, and C. The reactions at these points will be:

A winch drum is pin-connected at its center C. A pawl AB acts as a two-force member to prevent rotation. This means the force exerted by the pawl on the winch is...

When is the assumption that a body remains 'rigid' under load generally acceptable in equilibrium analysis?

What is the consequence of having all reactive forces in a 2D system be parallel?

How many unknown reaction components exist for a single smooth pin in a 3D system?

An unloaded platform with a weight of 1962 N is suspended by a pin at A and a cable at B. The cable force T and pin reactions Ax and Ay must maintain equilibrium. If half the total reaction magnitude is developed at A and half at B, this implies that:

When drawing a free-body diagram, couple moments are treated as free vectors. What does this mean?

A 300 N force is applied vertically to a lever, which is pinned at B and connected to a horizontal short link at A. What is the force in the link at A if the lever arms are equal?

Why must the analysis of a 3D system supported by properly aligned single bearings often not include the couple-moment components shown in Table 5-2?

An outrigger ABC is used to support a backhoe. It is supported by a smooth bearing shoe at A, a pin at C, and a two-force hydraulic cylinder at B. Which statement correctly describes the reaction at A?

A boom AC on a lift is supported by a pin at A and a two-force hydraulic cylinder BC. A load P acts at C. The FBD of the boom would show: