22: Lecture Equilibrium and Elasticity
Phys 2101 Fall 2003 Gabriela Gonzlez
Equilibrium: example
A uniform plank with a length L=6m and weight 500N, rests on the ground an against a frictionless roller at the top of a wall of height h=3m. The plank remains in equilibrium for any value of the angle q larger or equal to 70o, but slips is the angle is smaller than70o. Find the coefficient of static friction between the plank and the ground.
2
Example
A thin horizontal bar AB of negligible weight and length L is hinged to a vertical wall at A by a think wire BC that makes an angle q with the horizontal. A load of weight W can be moved anywhere along the bar; its position is defined by the distance x from the wall to its center of mass. As a function of x, find (a)the tension in the wire, and the (b)horizontal and (c)vertical components of the force on the bar from the hinge at A.
3
Elasticity: Stress and strain
Strain L/L = Stress= F/A Young's modulus: E=stress/strain Strain = x/L Stress= F/A Shear modulus: G=stress/strain Strain = V/V Stress= pressure p(=F/A) Bulk modulus: B=stress/strain
tensile stress
shearing stress
hydraulic stress
4
Example
The graph shows the stress-strain curve for quartzite. What is the Young's modulus? Yield strength: modulus is no longer constant, and the forces produce permanent deformation
5
Example
A mine elevator is supported by a single steel cable 3.2 cm in diameter. The total mass of the elevator cage plus occupants is...