Forces Chapter 4

Forces A push or a pull  Gravitational  Electromagnetic  Weak  Strong

Sir Isaac Newton

Newton’s First Law  An object in motion remains in motion and an object at rest remains at rest unless acted on by an outside force.  Sometimes called the Law of Inertia  Examples  Sudden braking  Flooring it  Seeing stars

Inertia  A body’s tendency to keep doing what it’s already doing  Measured by mass  Does not need gravitational force.

Newton’s Second Law  The acceleration of an object is directly proportional to the force on the object and inversely proportional to the mass.

Units  Newtons  English equivalent is pounds  4.45N=1lb

Practice  A 2988kg elephant accelerates on a skateboard at a rate of 2.7m/s 2. If the elephant is being pushed with a 10,000N force, what is the force of friction?  A 58.7N force is applied to a go kart to get it started. If the car starts from rest and accelerates for 4.0s covering a distance of 7.8m, what is the mass of the kart?

Newton’s Third Law  When one object exerts a force on a second object, the second object exerts a force on the first of equal magnitude and opposite direction  Action-reaction pairs  Switch the nouns

Weight  Weight and gravitational force are the same thing.  Since acceleration due to gravity (g) is known, we can define weight as:  In general, we will take care of directional information (positives and negatives) in the problem itself, so we will use +9.8m/s 2 instead of -9.8m/s 2

Skydiving and Terminal Velocity

Practice Problems  A skydiver reaches a terminal velocity of 55m/s when in free fall. If the skydiver has a mass of 78kg, how much force is air resistance providing?  When starting up the elevator, a rider experiences an acceleration of 1.2m/s 2. If the force from the elevator floor is 650N, what is the mass of the rider?

Normal Force  Force pushing up from a surface  When vertical acceleration is zero and the only two vertical forces are gravity and normal force, normal force and gravity are equal.  Scales read normal force  Elevators  Weightlessness (Newton’s Mountain) Newton’s MountainNewton’s Mountain

Friction  Depends only on the surfaces, not on velocity  Kinetic and static friction  Depends on two things, normal force of the object and the combination of surfaces  Coefficient of friction, µ equals the ratio of frictional force to normal force.

Practice  A 16.8 kg crate is pushed horizontally along the floor with a force of 207N. If the coefficient of friction is 0.62, what is the acceleration of the crate?

 A sled is pulled across the snow with a constant velocity. If the sled has a mass of 32.1kg and the coefficient of kinetic friction is 0.14, what is the magnitude of the pull?

 A bunch of guys try to push a car out of the mud. They push harder and harder until it becomes unstuck and then push with a constant force. If the coefficient of static friction is 0.54 and the coefficient of kinetic friction is 0.40, what is the acceleration of the car once it starts moving?

 A crate of chickens is pulled with 145N of force with a rope that is inclined 30° up from the horizontal. If the crate has a mass of 35kg and the coefficient of friction between the floor and the crate is 0.43, what is:  The normal force on the crate?  The acceleration of the crate, assuming it accelerates horizontally.

Tension  Upward force coming from a string or rope.  All vertical ropes supporting an object account for an equal amount of force unless specified otherwise.

Atwood Machine Problems  Assumptions a 1 = a 2 F T1 = F T2  Pulley switches which direction is positive.  Consider the direction of motion of the box to be the positive direction. m1m1 m2m2 If mass 1 is 5kg and mass 2 is 7kg, what is the acceleration of the system?

Box 1 FgFg FTFT a

Box 2 FgFg FTFT a

Putting it together

Putting it together cont.

Practice Problem  m 1 =8kg  m 2 =4kg  Find F T m1m1 m2m2

Sign Problems  Equilibrium-the state where all forces are balanced and acceleration is zero.  Includes both stationary and constant velocity cases.

1 st Example  If the sign has a mass of 15kg, what is the tension in the string? What is the force the beam exerts on the sign?  Assume equilibrium.  One component at a time.

Set up equilibrium case FyFy FxFx FTFT 23 FgFg F beam

Equilibrium case for vertical

Equilibrium case for horizontal

Practice Problem 2  Find the tension in each rope. T1T1 T2T2

Break up Components F1F1 F2F2 F x1 F x2 F y1 F y2 FgFg

Horizontal Pieces  Since the sign isn’t accelerating horizontally, we can use: F x1 F x2 F y1 F y2 FgFg

Vertical Pieces  Since the sign isn’t accelerating vertically, we can use: F x1 F x2 F y1 F y2 FgFg

Putting the two together

Putting the two together cont.

Ramp Problems

Practice Problems  A box slides down a frictionless ramp. If the box has a mass of 12kg and the ramp is inclined at an angle of 32 degrees, what is the acceleration of the box?  A 76kg box slides down a ramp inclined at 21 degrees. If the acceleration of the box is 1.2m/s 2, what is the coefficient of friction between the box and the ramp?

Random Practice Problems  A 28kg box is pulled at an angle of 18 o up from the horizontal with a force of 145N. If the coefficient of friction between the floor and the box is.32, what is the acceleration of the box?

 A dead pig has a µ k of.21 and a µ s of.43 when sitting on a book cover, how far will the book cover need to be tilted to start the pig carcass moving? Once it starts moving, how quickly will it accelerate?

 m 1 =13kg  m 2 =9kg  μ k =.11  What is a?