Force System Resultants

What is the term for the tendency of a force to rotate a body about a point not on the line of action of the force, often referred to as a torque?

If a 100 N force is applied perpendicularly to the handle of a wrench at a distance of 2 m from a bolt at point O, what is the magnitude of the moment about point O?

Which rule is used to establish the sense of direction of a moment vector in two or three dimensions?

What is the result of the cross product of two parallel vectors A and B?

According to the laws of operation for the vector cross product, which of the following relationships is correct?

What is the result of the cross product of the Cartesian unit vectors i x j?

The moment of a force F about a point O can be expressed using the vector cross product as Mo = r x F. What does the vector r represent in this equation?

What does the Principle of Transmissibility state regarding a force applied to a rigid body?

Varignon's theorem, also known as the principle of moments, states that the moment of a force about a point is equal to what?

A force F has x and y components. The force is applied at a point with coordinates (x, y). What is the scalar expression for the moment of F about the origin O, according to the principle of moments?

How is the moment of a force F about a specified axis 'a' calculated using the scalar triple product?

In the determinant form for the moment about an axis, Ma, what do the elements of the first row of the 3x3 determinant represent?

What is the definition of a couple?

Which statement best describes the nature of a couple moment?

Two parallel, oppositely directed forces of 50 N are separated by a perpendicular distance of 0.4 m. What is the magnitude of the couple moment they produce?

When simplifying a system of forces and couple moments to an equivalent system at a point O, what is the resultant force FR equal to?

When simplifying a system of forces and couple moments to an equivalent system at a point O, what is the resultant couple moment (MR)O equal to?

Under what condition can a general force and couple system be further reduced to a single resultant force?

For a coplanar force system, how can the perpendicular distance 'd' of the single resultant force FR from a point O be found?

What is the simplest system that can represent any general 3D force and couple moment system, which consists of a resultant force and a collinear couple moment?

For a distributed loading w(x) along a beam, how is the magnitude of the resultant force FR determined?

Where does the line of action of the resultant force FR of a distributed load w(x) pass through?

A beam of length 9 m has a triangular distributed load, starting at 0 N/m at x=0 and increasing linearly to 1440 N/m at x=9 m. What is the magnitude of the resultant force FR?

For a triangular distributed load that starts at 0 at x=0 and increases to a maximum at x=L, where is the centroid (and thus the line of action of the resultant force) located?

In the vector cross product C = A x B, what is the magnitude of C defined as?

If a force of 40 lb is applied to a bent rod such that its total lever arm about point O is (4 ft + 2 cos 30 deg ft), what is the resulting moment about O?

If the cross product of two vectors A and B is C = A x B, what is the direction of vector C relative to vectors A and B?

A rod is acted on by four forces about point O. The moments are: -50N(2m) from a 50N force, +60N(0) from a 60N force, +20N(3sin30m) from a 20N force, and -40N(4m + 3cos30m) from a 40N force. What is the resultant moment about O?

What is the result of the vector cross product j x k?

In vector analysis, what is the determinant used for when evaluating A x B for vectors A = Ax*i + Ay*j + Az*k and B = Bx*i + By*j + Bz*k?

A force F acts at a point A on a rigid body. When finding the moment of F about another point O, the principle of transmissibility allows the moment to be calculated as rB x F, where rB is the position vector from O to a point B. What must be true about point B?

Two forces, F1 and F2, act on a rod. The moment they create about the flange at O is the sum of the moments of each force. If F1 = {-60i + 40j + 20k} lb acts at rA = {5j} ft and F2 = {80i + 40j - 30k} lb acts at rB = {4i + 5j - 2k} ft, what is the resultant moment about O?

When a scalar analysis is used for a 2D problem, what is the convention for the sign of a moment that causes a counter-clockwise rotation?

If a force F passing through point B creates a moment about point A, and the calculation using vector analysis yields a negative scalar for Ma, what does this indicate about the direction of the moment vector Ma?

A 5 kN force is applied to a rod at 3m from the origin O. The angle of the force is 45 degrees, and the angle of the rod is 30 degrees from the x-axis. Using the principle of moments with Fx = 5cos45 and Fy = 5sin45, and lever arms dx = 3cos30 and dy = 3sin30, what is the moment about O?

What is a key advantage of using a Cartesian vector analysis for solving three-dimensional moment problems compared to a scalar approach?

A resultant couple moment MR is the result of summing two couple moments M1 and M2. How is MR determined?

A plate has three couples acting on it. The first is a 200 lb couple with a 4 ft arm, acting clockwise. The second is a 450 lb couple with a 3 ft arm, acting counter-clockwise. The third is a 300 lb couple with a 5 ft arm, acting clockwise. What is the resultant couple moment?

For which type of force system is the resultant moment (MR)O independent of the location of the point O?

For a distributed loading problem where the loading diagram is a trapezoid, what is a valid method for finding the resultant force and its location?

A force F = {6i + 8j + 10k} N creates a moment about point O of Mo = {-14i + 8j + 2k} N·m. If this force passes through a point with an x coordinate of 1 m, what must be true about the relationship between Mo, F, and the perpendicular distance d from O to the line of action of F?

A force of F = 200 N is applied to a door handle. To find the moment produced by this force about the hinged axis (the x-axis) of the door, what quantity is needed?

A couple is applied to a steering wheel. The first case uses 30 N forces with a 0.4 m separation. The second case uses 40 N forces with a 0.3 m separation. What is true about the couple moments produced?

If a force's line of action passes through the axis about which a moment is to be determined, what is the value of the moment?

What is the primary reason that in two-dimensional problems, a scalar analysis for moments is often preferred over a vector analysis?

A pipe column is subject to a couple M1 from forces at A and B, and a couple M2 from forces at C and D. M1 is found to be {60i} N·m. M2 is found to be {22.5j + 30k} N·m. What is the resultant couple moment MR?

When replacing a force and couple system with an equivalent resultant force FR and couple moment (MR)o, which of the following is true?

A beam is subjected to a 3 kN force and a 5 kN force. The 3 kN force is at 30 degrees to the horizontal. The 5 kN force has a 3-4-5 slope. A 4 kN force also acts downwards. When summing forces, what is the y-component of the resultant force, (FR)y?

If a structural member is subjected to a couple moment M and two forces F1 and F2, what is the general formula for the resultant moment MRo about the origin O?

A jib crane is loaded with three coplanar forces: 175 lb horizontally, 60 lb downwards, and a 250 lb force at a 3-4-5 slope. What is the y-component of the resultant force, FRy, assuming up is the positive y-direction?