Statics: Master the Fundamentals of Force and Equilibrium

Question 1

The moment of a force about a point is defined as the force multiplied by the:

Accepted Answer

Distance from the point to the line of action of the force

Answer

Distance from the point to the point of application of the force

Answer

Sine of the angle between the force and the distance from the point to the line of action of the force

Answer

Cosine of the angle between the force and the distance from the point to the line of action of the force

Question 2

A beam is subjected to three forces: F1 (100 N to the right), F2 (50 N to the left), and F3 (75 N to the right). Determine the magnitude and direction of the net force acting on the beam.

Accepted Answer

125 N to the right

Answer

25 N to the left

Answer

225 N to the right

Answer

75 N to the left

Question 3

In a cantilever beam fixed at one end, where does the maximum deflection occur?

Accepted Answer

Free end

Answer

Fixed end

Answer

Center of the beam

Question 4

A rigid body is in static equilibrium under the influence of two forces, F1 and F2. Which statement accurately describes the relationship between the magnitudes and directions of F1 and F2?

Accepted Answer

F1 and F2 are equal in magnitude and opposite in direction.

Answer

F1 and F2 are equal in magnitude and in the same direction.

Answer

F1 and F2 are perpendicular to each other.

Answer

The magnitudes of F1 and F2 cannot be determined without additional information.

Question 5

For a particle to be in equilibrium, which condition must be satisfied?

Accepted Answer

The net force acting on the particle must be zero.

Answer

The net moment acting on the particle must be zero.

Answer

The particle must be stationary.

Question 6

In statics, what two conditions must be met for a rigid body to be in equilibrium?

Accepted Answer

The sum of all forces acting on the body is zero, and the sum of all moments acting on the body about any point is zero.

Answer

The net force acting on the body is equal to the net moment acting on the body.

Answer

The body is at rest, and its velocity is constant.

Question 7

An object is initially at rest on a horizontal surface. Which of Newton's laws of motion describes what will happen to this object?

Accepted Answer

It will remain at rest until an external force acts on it.

Answer

It will start moving in a random direction.

Answer

Its momentum will continuously change.

Answer

Its velocity will continuously increase due to Earth's gravity.

Question 8

A rigid body is in equilibrium under the influence of four forces. Which of the following statements accurately describes the forces acting on the body?

Accepted Answer

The net force acting on the body is zero, and the net moment about any point is also zero.

Answer

The forces are parallel and have equal magnitudes.

Answer

The forces are concurrent and have equal magnitudes.

Answer

The forces are equal and opposite.

Question 9

For a rigid body to be in equilibrium, what conditions must be met?

Accepted Answer

The net force and net moment acting on the body must be zero.

Answer

The body must be moving with constant speed.

Answer

The body must be rotating with constant angular speed.

Answer

The sum of the forces acting on the body must equal the sum of the moments acting on the body.

Question 10

For a rigid body to be in equilibrium, which conditions must be met?

Accepted Answer

The net force acting on the body is zero, and the net moment about any axis is zero.

Answer

The net force acting on the body is zero.

Answer

The net moment about any axis is zero.

Answer

The sum of the forces in each coordinate direction is zero.

Question 11

A rigid body is subjected to two forces, F1 and F2, acting at points A and B, respectively. Calculate the moment of the force F1 about point B.

Accepted Answer

F1 multiplied by the magnitude of vector AB

Answer

F2 multiplied by the magnitude of vector AB

Answer

F1 multiplied by the magnitude of vector BA

Answer

F2 multiplied by the magnitude of vector BA

Question 12

Define the shear force in a beam.

Accepted Answer

Algebraic sum of transverse forces acting on the beam

Answer

Algebraic sum of moments acting on the beam

Answer

Force perpendicular to the beam

Answer

Force parallel to the beam

Question 13

What quantity does the coefficient of friction between two surfaces represent?

Accepted Answer

Ratio of frictional force to normal force

Answer

Ratio of normal force to frictional force

Answer

Angle between normal force and frictional force

Answer

Coefficient of restitution between the surfaces

Question 14

A simply supported beam with a span of L is subjected to a uniformly distributed load of intensity w. Determine the maximum deflection at the center of the beam.

Accepted Answer

wL^4/8EI

Answer

wL^3/24EI

Answer

wL^2/12EI

Answer

wL/8EI

Question 15

A rigid body is in equilibrium under the influence of four forces, F1, F2, F3, and F4. Which of the following conditions must be satisfied for the body to be in equilibrium?

Accepted Answer

The net force acting on the body must be zero.

Accepted Answer

The net moment acting on the body about any point must be zero.

Answer

The forces must intersect at a single point.

Answer

The magnitude of the resultant force must be non-zero.

Question 16

A uniform beam is supported by two vertical cables, each with a tension of 500 Newtons. What is the weight of the beam?

Accepted Answer

1000 N

Answer

250 N

Answer

500 N

Answer

1500 N

Question 17

Which of the following is a scalar quantity?

Accepted Answer

Temperature

Answer

Velocity

Answer

Force

Answer

Acceleration

Question 18

A truss is a structure that uses triangles to distribute loads. Which of the following statements about trusses is true?

Accepted Answer

Trusses are used in bridges and buildings

Answer

Trusses are always statically determinate

Answer

Trusses can only support vertical loads

Answer

Trusses are not efficient structures

Question 19

A torque of 10 Newton-meters is applied to a rigid body. What is the angular acceleration of the body if its moment of inertia is 2 kilogram-meters squared?

Accepted Answer

2 rad/s²

Answer

5 rad/s²

Answer

10 rad/s²

Answer

20 rad/s²

Question 20

A rigid body is in equilibrium when:

Accepted Answer

Both (a) and (b) are true

Answer

The net force acting on the body is zero

Answer

The net torque acting on the body is zero

Answer

Neither (a) nor (b) is true

Question 21

A rigid body is subjected to a torque. Which of the following is true about the body's motion?

Accepted Answer

It will rotate

Answer

It will translate

Answer

It will do both translation and rotation

Answer

It will remain stationary

Question 22

The moment of inertia of a body about a certain axis is a measure of the body's:

Accepted Answer

Resistance to angular acceleration

Answer

Mass

Answer

Size

Answer

Speed

Question 23

Which of the following is NOT a necessary condition for equilibrium?

Accepted Answer

Constant velocity

Answer

Zero net force

Answer

Zero net moment

Answer

Stationary body

Question 24

Two 500 N vertical forces support a beam 2 meters apart. What is the maximum bending moment in the beam?

Accepted Answer

1000 Nm

Answer

250 Nm

Answer

500 Nm

Answer

2000 Nm

Question 25

A particle in equilibrium experiences three forces. Which statement is accurate?

Accepted Answer

Form a closed polygon

Answer

Parallel forces with equal magnitudes

Answer

Perpendicular forces with equal magnitudes

Answer

Equal magnitudes, opposite directions

Question 26

Two couples act on a rigid body in equilibrium. What is the relationship between their magnitudes?

Accepted Answer

Equal

Answer

Opposite

Answer

Proportional to the distance between forces

Answer

Inversely proportional to the distance between forces

Question 27

Which force is NOT conservative?

Accepted Answer

Frictional force

Answer

Gravitational force

Answer

Elastic force

Answer

Electric force

Question 28

For a rigid body in equilibrium under the action of forces that all lie in the same plane, what is the net moment of the forces about any point in that plane?

Accepted Answer

Zero

Answer

Equal to the moment of the largest force

Answer

Equal to the sum of the moments of all clockwise forces

Question 29

A simply supported beam of length **L** carries a uniformly distributed load of intensity **w**. The maximum deflection of the beam is:

Accepted Answer

wL^4/(8EI)

Answer

wL^3/(24EI)

Answer

wL^2/(16EI)

Answer

wL/(4EI)

Question 30

A rigid body is in equilibrium under the action of three forces, F1, F2, and F3. Which of the following statements is true about the forces acting on the body?

Accepted Answer

The sum of the forces is zero.

Accepted Answer

The sum of the moments of the forces about any point is zero.

Answer

The forces are all equal in magnitude.

Answer

The forces are all acting in the same direction.

Question 31

How does increasing the moment of inertia of a beam affect its deflection under constant load and boundary conditions?

Accepted Answer

Decreases deflection

Answer

Increases deflection

Answer

No effect on deflection

Question 32

For a rigid body in equilibrium under the action of coplanar forces, what is the net moment of the forces about any point in the plane?

Accepted Answer

Zero

Answer

Equal to the moment of the resultant force about that point

Answer

Equal to the sum of the moments of the forces about that point

Answer

Equal to the moment of the weight of the body about that point

Question 33

Which of the following is a necessary condition for a body to be in equilibrium?

Accepted Answer

Both options A and B

Answer

The sum of all forces acting on the body is zero

Answer

The sum of all moments acting on the body is zero

Question 34

What is a couple?

Accepted Answer

Two equal and opposite forces acting at a distance

Answer

Two parallel forces acting in the same direction

Answer

Two forces acting at an angle to each other

Question 35

What is the moment of inertia of a rectangular area about its central axis perpendicular to its length?

Accepted Answer

Area * (width^2 + height^2) / 12

Answer

Area * (width^2 - height^2) / 12

Answer

Area * (width + height) / 12

Question 36

What is a free body diagram?

Accepted Answer

A diagram showing all forces acting on a body

Answer

A diagram showing all forces and moments acting on a body

Answer

A diagram showing the forces and moments acting on a body relative to a fixed point

Question 37

What does the principle of superposition state?

Accepted Answer

The effect of multiple forces acting on a body is the same as the sum of the effects of each force acting alone

Answer

The moment of a force about a point is equal to the sum of the moments of its components about that point

Answer

The centroid of a body is located at the average of the centroids of its parts

Question 38

What is a truss?

Accepted Answer

A structure that uses triangulated elements to transfer loads

Answer

A structure that is always statically indeterminate

Answer

A structure that is typically used in bridges and roofs

Question 39

For a rigid body to be in equilibrium, which of the following conditions must BOTH be satisfied?

Accepted Answer

The resultant force acting on the body is zero, and the resultant moment acting on the body about any axis is zero.

Answer

The resultant force acting on the body is zero, and the linear velocity of the body is constant.

Answer

The resultant moment acting on the body about any axis is zero, and the angular velocity of the body is constant.

Answer

The resultant force acting on the body is non-zero, and the resultant moment acting on the body about any axis is non-zero.

Question 40

In a beam loaded in bending, the shear force at a section represents:

Accepted Answer

The internal force resultant of the transverse forces acting on the section

Answer

The axial force acting on the cross-section

Answer

The bending moment acting on the section

Answer

The external force applied at the end of the beam

Question 41

A truss is a structure composed of members connected at joints. Which of the following is NOT a type of truss?

Accepted Answer

Vierendeel truss

Answer

Pratt truss

Answer

Howe truss

Answer

Warren truss

Question 42

A force of 100 N acts at a point A. Calculate the moment of this force about a point B, which is 2 m from point A.

Accepted Answer

200 Nm

Answer

25 Nm

Answer

100 Nm

Answer

50 Nm

Question 43

Define a truss.

Accepted Answer

A truss is a structure composed of rigid members connected at their ends by pin joints.

Answer

A truss is a structure composed of rigid members connected at their ends by rigid joints.

Answer

A truss is a structure composed of flexible members connected at their ends by pin joints.

Question 44

Which of the following is a defining characteristic of a truss structure?

Accepted Answer

A truss can only support loads applied at its joints

Answer

A truss can only support loads applied at its midpoints

Answer

A truss can only support loads applied at its ends

Answer

A truss can only support loads applied along its length

Question 45

For a rigid body to be in equilibrium, what two conditions must be satisfied?

Accepted Answer

The sum of the forces acting on the body is zero, and the sum of the moments acting on the body is zero

Answer

The sum of the forces acting on the body is zero

Question 46

A wrench with a length of 200 mm is used to tighten a bolt. The coefficient of friction between the wrench and the bolt is 0.2. Determine the minimum force that must be applied to the end of the wrench to prevent it from slipping.

Accepted Answer

100 N

Answer

50 N

Answer

200 N

Question 47

A beam with a length of 6 m is supported by a pin at one end and a roller at the other end. A concentrated load of 10 kN is applied at the mid-span of the beam. Determine the reaction force at the pin.

Accepted Answer

7.5 kN

Answer

10 kN

Answer

5 kN

Answer

12.5 kN

Question 48

A rigid body is in equilibrium if:

Accepted Answer

Both the net force and net moment acting on it are zero.

Answer

Only the net moment acting on it is zero.

Answer

Only the net force acting on it is zero.

Question 49

A couple consists of:

Accepted Answer

Two equal and opposite forces that do not act along the same line of action.

Answer

Two equal and opposite forces that act along the same line of action.

Answer

A single force acting on a rigid body.

Question 50

The radius of gyration of an area about an axis is defined as:

Accepted Answer

The square root of the ratio of the moment of inertia about the axis to the area.

Answer

The ratio of the moment of inertia about the axis to the area.

Answer

The square of the ratio of the area to the moment of inertia about the axis.

Question 51

The fundamental principle governing static equilibrium states that for a rigid body to be in equilibrium, the sum of all forces acting on it must be zero and the sum of the moments about any point must also be zero. What is this principle known as?

Accepted Answer

Principle of Equilibrium

Answer

Principle of Virtual Work

Answer

Principle of Superposition

Question 52

A 200 kg block is suspended from a cable attached to the ceiling. Calculate the tension in the cable.

Accepted Answer

1962 N (9.81 m/s² * 200 kg)

Answer

1000 N

Answer

2000 N

Answer

981 N

Question 53

A force of 500 N is applied perpendicular to a lever at a distance of 0.75 m from the pivot point. Determine the moment created by the force.

Accepted Answer

375 Nm (500 N * 0.75 m)

Answer

250 Nm

Answer

1000 Nm

Answer

500 Nm

Question 54

In the analysis of trusses, which assumption is made about the forces acting on the members?

Accepted Answer

Members are assumed to be two-force members.

Answer

Members are assumed to be continuous and solid.

Answer

Members are assumed to be three-force members.

Answer

Members are assumed to be flexible.

Question 55

The method of joints is a technique used to analyze forces in trusses. Which of the following statements about the method of joints is accurate?

Accepted Answer

It involves analyzing the equilibrium of forces at each joint.

Answer

It is only applicable to simple trusses with a limited number of joints.

Answer

It necessitates knowledge of the internal forces in all members.

Question 56

A simply supported beam is subjected to a concentrated load at its midpoint. Describe the shape of the resulting bending moment diagram.

Accepted Answer

Triangular, with the peak at the point of concentrated load

Answer

Constant throughout the beam

Answer

Linearly increasing from one end to the other

Answer

Parabolic, with the peak at the center

Question 57

What is the key distinction between statically determinate and statically indeterminate structures?

Accepted Answer

Statically determinate structures can have all internal forces determined using equilibrium equations alone.

Answer

Statically indeterminate structures are always stronger than determinate structures.

Question 58

To move a large, heavy object across a floor, which method would minimize the force required to initiate movement?

Accepted Answer

Using a rolling cart with wheels

Answer

Dragging the object directly across the floor

Answer

Lifting the object vertically

Question 59

A 100 kg crate is suspended by two cables. One cable makes a 30-degree angle with the horizontal, and the other makes a 60-degree angle. What is the tension in the cable at the 30-degree angle?

Accepted Answer

866 N

Answer

500 N

Answer

1000 N

Question 60

A cable with a cross-sectional area of 10 mm² is subjected to a tensile force of 5 kN. If the cable's Young's modulus is 200 GPa, what is the elongation of the cable?

Accepted Answer

2.5 mm

Answer

0.25 mm

Answer

10 mm

Answer

5 mm

Question 61

A beam supported at both ends carries a uniformly distributed load. Which internal force is NOT present in the beam?

Accepted Answer

Torsion

Answer

Shear Force

Answer

Axial Force

Answer

Bending Moment

Question 62

A ladder leans against a frictionless wall. What is the direction of the reaction force at the point where the ladder contacts the wall?

Accepted Answer

Horizontal, perpendicular to the wall

Answer

Vertical, upwards

Answer

There is no reaction force since the wall is frictionless

Answer

At an angle, dependent on the ladder's weight

Question 63

Two forces, one of 10 kN and another of 15 kN, act on a particle. What is the range of possible magnitudes for their resultant force?

Accepted Answer

5 kN to 25 kN

Answer

0 kN to 25 kN

Answer

15 kN to 25 kN

Answer

10 kN to 15 kN

Question 64

For a system of forces acting on a rigid body to be in equilibrium, which condition MUST be satisfied?

Accepted Answer

Both the sum of forces and the sum of moments must be zero.

Answer

The sum of forces must be zero.

Answer

The sum of moments must be zero.