1. Force and Moment Vectors
Steven A. Jones
9/20/2018

2. Basics Force is rate of change of momentum
If you push on a wall, it exerts an equal force on you
Force is in Kg m/s2 or Newtons
Can also be g cm/s2 or dynes
A Newton is a little less than ¼ lbs, or a little less than the weight of ½ cup of water.
A dyne is 5 orders of magnitude smaller.
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3. Forces Forces add as vector quantities Can draw a free body diagram
All forces must balance one another
Some forces may be discrete, some distributed.
With distributed forces, often concerned with the resultant force.
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4. Forces Normal forces act normal to a surface (e.g. pressure).
Tangential forces act tangentially to the surface (e.g. frictional forces).
Tensile & compressive forces may have different consequences:
Concrete – works well in compression, not so well in tension.
A bicycle spoke works poorly in compression.
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5. Forces Coplanar Forces – in the same plane
Collinear Forces – along the same line
Concurrent Forces – lines of action pass through the same point.
Parallel Forces – act in the same direction
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6. Gravity Gravity – the least well-understood force On Earth:
g = 9.81 m/s2
g = 981. cm/s2
g = 32.2 ft/s2
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7. Distributed Forces
A distributed load in a free body can be replaced with it a point load at the center of mass. p P
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8. Friction F=cN Coefficient differs for sliding and static friction.
Coefficient must also depend on velocity of motion (otherwise it would require just as much force to slide a refrigerator at 100 ft/s as at 1 ft/s).
Friction burns up energy.
We consider it a nuisance, but just try ice skating without it.
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9. Moment F1 F2 r F1 and F2 apply the same moment around p r’ p
Can translate F1 anywhere along its line of action. r’ p
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10. Moment Direction of moment is perpendicular to the plane.
Right-hand rule gives sign of direction.
Resultant momentum is sum of momenta
A couple is caused by 2 forces of same magnitude and opposite direcdtion.
Magnitude of moment of a couple is F times distance. (True of any point affected by the couple).
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11. Mechanically Equivalent Systems
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12. Statics Concepts
Sum of forces must be zero (translational equilibruim)
Sum of moments must be zero (rotational equilibrium)
The above gives 6 equations in space.
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13. Types of problems solved in Statics
Truss problems
Beam problems
Machine problems
Rope/Pully problems
Friction Problems (ramp problems)
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14. Types of Problems Solved in Mechamics of Materials
Torsion problems
Elastic beam problems (force along the beam length)
Finding V and M in a beam
Location of maximum stress for a beam
Beam deflection problems
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15. To Review Center of Mass I for a beam J for a shaft Q for a beam
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16. Shaft J is the polar moment of inertia G is the shear modulus
Principle stresses are at 45 degrees
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17. Beams: Flexural Stress
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18. Beams: Shear Stress
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