Static and Rotational Equilibrium

Static and Rotational Equilibrium Ch4: Sections 1,2,6-11 Ch9: Sections 1-3

What causes objects to start moving?What causes a change in speed or direction of an object?

Introducing Forces • A force is a push or pull on an object. • When forces are unbalanced, they cause an object to accelerate, or to change its velocity by speeding up, slowing down, or changing direction.

Newton’s 1st Law (Law of Inertia) • If there is zero net force on a body, it cannot accelerate, and therefore must move at constant velocity. This means • the body cannot turn. • the body cannot speed up. • The body cannot slow down.

Measuring Force • Newton (N): SI unit of force • N = 1kg * 1 m/s2 • 1 lb = 4.448 N • 1 N = 0.225 lb • Spring scale or force meter

Translational vs. Static Equilibrium Translational ΣF=0 or Fnet=0 May be in motion, but must be constant Static ΣF=0 or Fnet=0 Object at rest

Types of Forces • Contact Forces: Physically touching • Normal • Friction • Tension • Spring • Field Forces • Magnetic • Gravitational • Electrical

Normal force • Keeps one object from penetrating into another object • Always perpendicular to a surface • Exactly cancels out the components of all applied forces that are perpendicular to a surface. • Can increase in magnitude (ie: pushing down harder & harder on a book on a table)

Force Diagram Free Body Diagram FN FN Physics Book FG FG Draw the forces for a physics book resting on a table

Normal Force • Not necessarily always opposite the Fg

Mass versus Weight • Mass is inertia, or resistance to acceleration. • Weight and mass are not equivalent! • Weight is gravitational force, which is equal to mgnear the earth’s surface. • Newton’s Law of Universal Gravitation

Where would you weigh more? • Walking in New Orleans • Mountain climbing on Mt. Everest • In an airplane traveling 4 miles above Montana • In an airplane traveling 4 miles above Singapore Answer: New Orleans because it’s closer to the center of the earth

Weight Vector Quantity: Force of gravity exerted by Earth Scalar Quantity: Magnitude of this force (weight) Weight = Fg = mg

Problem: derive an expression for the normal force of a box on a flat table.

 Problem: Derive an expression for the normal force of a box sitting on a ramp.

F = 20 N 40o 6.0 kg Problem: Derive the normal force for the box in the picture below. The box is sitting on the floor, but is being pulled by the force shown. Ignore friction.

Force of Friction • Force that opposes motion • Parallel to surface • Opposite direction of movement

Static Frictionfriction opposing an object before it begins moving Greatest applied force without jug moving Fapplied = Fs,max Jug at rest Fnet =0 Small force applied Jug remains at rest Fapplied = Fs Applied force with jug moving Fapplied greater or equal to Fk

Kinetic Friction, Fk • Frictional force of 2 contact surfaces that are MOVING past one another • Less than static friction because adhesion has been overcome • Fnet = Fapplied – Fk

Which is easier?Push a chair across the floorPush a heavy desk across the floor • Force of friction is proportional to Fn

fuNEquation

Which is easier:Push a chair across a tile or carpeted floor? • Friction depends on the surfaces in contact • Coefficient of Friction (μ): ratio of the Ff to Fn Coefficients of Friction Materials Static Friction Kinetic Friction Steel on steel 0.74 0.57 Aluminum on steel 0.61 0.47 Wood on brick 0.60 0.45 Copper on steel 0.53 0.36 Rubber on concrete 1.0 0.80 Wood on wood 0.25 – 0.50 0.20 Glass on glass 0.94 0.40 Waxed wood on wet snow 0.14 0.10 Waxed wood on dry snow -- 0.040 Metal on metal (lubricated) 0.15 0.060 Ice on ice 0.10 0.030 Teflon on teflon 0.040 0.040 Synovial Joints in humans 0.010 0.0030

Problem: derive an expression for the normal force an eraser being pushed up against a whiteboard by a force F.

Problem: derive an expression for the normal force caused by an eraser being pushed up against a whiteboard by a force F.

A 24kg crate initially at rest on a horizontal floor requires 75N horizontal force to set it in motion. Find the coefficient of static friction between the crate and floor N I: SE (Static Equilibrium) ΣFx = 0 Fapp - Fs,max=0 Fapp= Fs,max Fs,max = μN E: ΣFy = 0 N – mg = 0 N = mg G: Draw FBD and label Fapp 75N Fs,max =μN mg (24kg)(9.81m/s2) S: S: U: μ also N and Fs

Problem: A 10-kg box rests on a ramp that is laying flat. The coefficient of static friction is 0.50, and the coefficient of kinetic friction is 0.30. • What is the maximum horizontal force that can be applied to the box before it begins to slide? • What force is necessary to keep the box sliding at constant velocity?

Tension • Pulling force • Arises when a rope, string, or other long thin material resists being pulled apart without stretching significantly. • Always pulls away from a body attached to a rope or string and toward the center of the rope or string.

Tension examples Note that the pulleys shown are magic! They affect the tension in any way, and serve only to bend the line of action of the force.

A physical picture of tension Imagine tension to be the internal force preventing a rope or string from being pulled apart. Tension as such arises from the center of the rope or string. It creates an equal and opposite force on objects attached to opposite ends of the rope or string.

Sample problem: A 1,500 kg crate hangs from a crane cable. • What is the tension in the cable when the crate is motionless? Ignore the mass of the cable.

Sample problem: An object acted on by three forces moves with constant velocity. One force acting on the object is in the +x direction and has a magnitude of 6.5 N; a second force has a magnitude of 4.4 N and points in the -y direction. Find the direction and magnitude of the third force acting on the object.

Sample problem: An object acted on by three forces moves with constant velocity. One force acting on the object is in the positive x direction and has a magnitude of 6.5 N; a second force has a magnitude of 4.4 N and points in the negative y direction. Find the direction and magnitude of the third force acting on the object.

FBD Worksheets

Betcha Can’t Lift 2kg!!!

A 85.0 kg traffic light is supported as shown. Find the tension in each cable. I: SE G: Draw Free Body Diagram U: T1 and T2

E: Resolve vectors into x and y components

S: We have two equations with two unknowns  solve for T1 S: Plug this value into the second equation:

Now we can find T1 by plugging the value of T2 into the first equation, which we already solved for T1.

A frictionless ramp is elevated at a 28.0 angle. A225N block rests on the surface and is kept from sliding down by a rope tied to a secure block as shown below. What is the tension on the rope? I: SE G: FBD U: T

2. Assign x and y coordinates

N Fgcosθ Block is sitting still so we know….Fx = 0 and Fy = 0 X direction: T is balanced by a force down the ramp

Springs • Hooke’s Law F = -kx • F: Force spring exerts • -: indicates that F is in opposite direction from stretched/compress displacement • k: Force or spring constant; indicates stiffness of spring • x: distance stretched/compressed • Only for small displacements

Slam Dunk:A 110k basketball player hangs motionless off the front rim that is defected down 15cm. Assume the rim can be approximated by a spring. Calculate the force constant k.

Assignment • APC: • #47,48,49,50

Announcements • Turn in • Handbook Forms (Matthew, Tyler, Nathan, Hunter) • Supplies (everyone stills owes something) • Complete the following problems: • 47,48,49,50,52,58 • MUST USE IGUESS METHOD on every prob. From now until the May 10th • Quiz MONDAY over • Summer Assignment • Anything covered this week • Ch 4 Reading • Ch 4 HW

Static and Rotational Equilibrium