Unit 12: Static Equilibrium and Elasticity
Ladders, beams, and hanging signs that don't move, plus the stress and strain of materials pushed toward their breaking point.
5 topics · 17 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Conditions for Static Equilibrium
- How it worksHow do a zero net force and a zero net torque together guarantee that a rigid object stays at rest?
- Worked exampleFind the required friction force at the base of a ladder leaning at 60 degrees against a frictionless wall, weighing 200 N.
- Common mistakeWhy isn't a zero net force alone enough to keep an extended object from starting to rotate?
- Going furtherWhat happens to a balanced object's equilibrium if you add a new force that passes through its center of mass?
Your turn1 of 2
A ladder of weight W leans against a frictionless wall, making an angle theta with the ground. Write an expression, in terms of W and theta, for the required friction force at its base.Center of Gravity
- How it worksHow does an object's center of gravity determine whether it tips over or stays balanced when tilted?
- Worked exampleFind the balance point of a seesaw with a 30 kg child 2 m from the pivot and a 40 kg child on the other side.
- Common mistakeWhy doesn't an object's center of gravity have to sit at its geometric center?
Your turn1 of 2
A child of mass m1 sits a distance d1 from the pivot of a seesaw. Write an expression, in terms of m1, d1, and m2, for the distance d2 at which a child of mass m2 must sit on the other side for balance.Solving Equilibrium Problems
- How it worksHow do you choose a pivot point to eliminate an unknown torque and solve an equilibrium problem in one step?
- Worked exampleFind the tension in each of two cables holding a 50 kg sign hung 0.5 m from one end of a 2 m beam.
- Going furtherWhat happens to the tension distribution on a beam as the load shifts closer to one of its two supports?
Your turn1 of 2
A sign weighing W hangs a distance d from the left end of a beam of length L, supported by vertical cables at each end. Write an expression, in terms of W, d, and L, for the tension in the RIGHT cable.Stress and Strain
- How it worksHow do stress and strain relate through a material's elastic modulus before anything permanently deforms?
- Worked exampleFind the strain in a 2 m steel rod that stretches by 0.5 mm under tension.
- Common mistakeWhy doesn't every material return to its original shape once a stretching force on it is removed?
Your turn1 of 2
A steel rod of length 3 m stretches by 0.684 mm under tension. What is the strain (as a dimensionless fraction)?Elastic Moduli and Material Failure
- How it worksHow do Young's modulus, the shear modulus, and the bulk modulus each describe resistance to a different kind of deformation?
- Worked exampleFind the stress on a wire of cross-sectional area 0.001 m2 under a tension force of 500 N.
- Common mistakeWhy doesn't a material's elastic limit mark the same event as its actual breaking point?
- Ties togetherHow does exceeding a material's elastic limit connect to permanent deformation instead of springing back?
Your turn1 of 2
A wire has a cross-sectional area of 3.63 square millimeters and carries a tension force of 1368 N. What is the stress on it, in pascals?