Dynamics & Equilibrium

Dynamics&Equilibrium Week 5

Contents • Overview • Gravitational Force • Equilibrium • FBD • Pulleys • Normal Force • Friction • Incline • Review

Overview Newton’s Laws • Inertia • F = ma • F1 + F2 = 0

Gravitational Force • When objects are near the earth’s surface, the gravitational force is F = mg. m mg

Equilibrium • The system is in equilibrium. ∑ F = 0 T – mg = 0 T = mg T m mg

Equilibrium (cont.) ∑ F = 0 ∑ Fx = 0 ∑ Fy = 0 y: 2TcosӨ - mg = 0 T = mg/2cosӨ Ө Ө T T m mg

Equilibrium (cont.) Ө1 Ө2 T1 T2 m mg

Free Body Diagram T1cosӨ1 T2cosӨ2 ∑ F = 0 ∑ Fx = 0 ∑ Fy = 0 Ө2 Ө1 T2sinӨ2 T1sinӨ1 T1 T2 m x: T1cosӨ1 – T2cosӨ2 = 0 y: T1sinӨ1 + T2sinӨ2 – mg = 0 mg

Pulleys • T is equal on both sides. • String is massless. • M > m T T m M mg Mg

Pulleys FBD M: Mg – T = Ma m: T – mg = ma Mg – mg = Ma + ma (M – m)g = (M + m)a a = (M – m)g/(M + m) T T M m Mg mg a a

Pulleys FBD (cont.) (M + m)a = Mg – mg (M + m)a = (M – m)g a = (M – m)g/(M + m) * Does not need tension! a Mg mg M m a Mg mg M + m

Normal Force N = mg N is always orthogonal to the surface. N m mg

Friction • Friction is caused by the forming and breaking of bonds between two surfaces. • It is mainly dependent on the chemistry of the materials.

Friction FBD f = μN *μ is a constant, depending on the chemistry of the materials *In general, f ≤ μN. N F f m mg

Quiz 1 • Apply a force F • System in equilibrium f = ? 3N 2kg

Quiz 1 f = mg f = 2(9.8) f = 20 N f 3N normal 2kg mg

Incline m Ө

Incline FBD N N f f m m mgcosӨ mg Ө mg Ө mgsinӨ

Incline FBD (cont.) • System in equilibrium y: f = mgsinӨ μN = mgsinӨ μ = mgsinӨ/N x: N = mgcosӨ μ = mgsinӨ/mgcosӨ μ = sinӨ/cosӨ μ = tanӨ N f m mgcosӨ mg Ө mgsinӨ

Review • Grav. force = mg • f = μN • N is orthogonal to the surface. • μ = tanӨ for an incline

Next Week • Work • Energy • Power

The End

Dynamics & Equilibrium