Statics Exam 1

Addition of Two Forces can be solved using what steps?

1. Parallelogram Law: 🔻Component forces add and yield resultant force that forms diagonal of parallelogram. 🔻If force is to be resolved into components along u and v axes; start from head of force and construct lines parallel to axis forming parallelogram. Sides of parallelogram represent Fu and Fv. 🔻Label all known and unknown force magnitudes and angles. 🔻Identify two unknowns as magnitude and direction of resultant force or the magnitude of its components. 🔻Draw triangle. 🔻From triangle magnitude of resultant force can be found using law of cos. Direction of is determined from law of sines.

Determine magnitude of Cartesian Vector?

A=sqrt(Ax^2+Ay^2+Az^2)

Concentrated Force?

Act at a point on a body.

The orientation of the x and y axes is?

Arbitrary, and their positive direction can be specified by the Cartesian unit vectors i and j.

Coplanar forces?

Coplanar force systems have all the forces acting in in one plane. They may be concurrent, parallel, non-concurrent or non-parallel.

Sense of Direction

Direction a vector is pointed.

i, j, k components of UA represent?

Directions of cosines of A. UA= cos(a)i+cos(b)j+cos(c)k

Rigid Body?

Does not deform under load.

How to determine the resultant of several coplanar forces?

Establish x, y coordinate system and resolve forces along axes.

Newton's 3rd Law?

For every action, there is an equal and opposite reaction. The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object.

The magnitude of the resultant force is determined how?

From the Pythagorean theorem.

How to find magnitude of resultant force?

Law of Cosines: C^2=A^2+B^2-2ABcos(c)

How are the magnitudes of two force components found?

Law of Sines

How to find direction of resultant force?

Law of sines: A/sin(a)=B/sin(b)=C/sin(c)

Scalar?

Positive or negative physical quantity that can be completely specified by its magnitude. eg: length, mass, time.

Magnitude of resultant force is determined by what theorem?

Pythagorean Theorem

The orientation of x and y axes is arbitrary and their positive directions can be specified by what?

The Cartesian unit vectors i and j.

Newton's 2nd Law?

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

The x and y components of the resultant force are what?

The algebraic addition of the components of all the coplanar forces.

The x and y components of the resultant force are?

The algebraic addition of the components of all the coplanar forces.

The direction of each force is specified by?

The angle its line of action makes with one of the axes, or by a slope triangle.

The direction of each force is specified by what?

The angle its line of action makes wth one of the axes, or by a slope triangle.

When components are sketched on x,y axes the direction can be determined how?

Trigonometry

How to form unit vector?

UA=(A/magnitude A) =(Ax/A)i+(Ay/A)j+(Az/A)k

Eq. for weight?

W=m*g

How is the direction of the of the resultant force determined?

When components are sketched on x and y axes, determined from trigonometry.

Concurrent force system?

all forces pass through a common point. In the previous case involving the application of two forces to a body, it was necessary for them to be colinear, opposite in direction, and equal in magnitude for the body to be in equilibrium.

Newton's 1st Law?

an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. It may be seen as a statement about inertia, that objects will remain in their state of motion unless a force acts to change the motion.

Newton's Law of Gravitational Attraction?

any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. F=(m1*m2)/r^2

Determine direction of Cartesian vector?

cos a=(Fx/magnitude F) cos b= (Fy/magnet F) cos c=(Fz/magnitude F)

Vector:

physical force that requires both magnitude and direction.

Line of Action

the line through the point at which the force is applied in the same direction as the vector F.

The resultant of several coplanar forces can be determined if?

x, y coordinate system is established and forces are resolved and the axes.