Inclined Planes A box slides down two smooth rails with no friction. Find the acceleration of the box.
FNFN F g = mg θ
Example: Forces on an Incline A 40 kg wagon is towed up a hill at an 18.5 o incline. The tow rope exerts a force of 140 N. The wagon starts from rest. How fast is the wagon going after 30 m? F app =140N
Givens, Unknowns and Models m = 40.0 kg F app = 140 N = 18.5 o x = 30 m v 0 = 0 v = ? This is constant force in the x direction (and constant acceleration) and equilibrium in y. mg mg cos( ) mg sin( ) F app FnFn
Method mg mg cos( ) mg sin( ) F app FnFn
This is about 11 mi/hr, a reasonable speed. It is positive, so the wagon moves uphill, as expected. Evaluate the Solution F app =140N
Friction Part 2
Discuss this question and be prepared to answer. What force pushes a car forward? Gravity pulls down. The normal force pushes upward. The car’s engine pushes on the wheels, but that is not an outside force.
Resistive Forces Resistive forces, such as friction and drag forces, are forces which oppose the relative motion of two surfaces, or a surface and a fluid. Friction occurs when two solid surfaces interact. Drag forces occur in fluids, i.e. liquids and gases.
Friction Friction is really just one component of the force between two surfaces. Friction is the force of interaction parallel to the surfaces. The perpendicular component is the normal force. We generally treat friction and the normal force as separate forces. FNFN F
Static and Kinetic Friction The amount of friction between an object and a surface depends on whether the object is moving relative to the surface. Static friction applies when the object is at rest relative to the surface. Kinetic friction applies when the object is moving relative to the surface.
Static Friction The force is equal to the applied force, until it exceeds a certain maximum. Once the maximum force of static friction is exceeded, the object breaks free and begins to slide.
Kinetic Friction Kinetic friction applies when the object is moving across the surface. The force of kinetic friction is typically less than the corresponding maximum force of static friction. In other words, once things are moving they are easier to keep moving. FNFN FkFk FgFg
Accelerating a car. The force the road applies to accelerate a car (speed up, slow down or change direction) is a frictional force. If the wheels do not slip, the friction can be treated as static friction. If the wheels slip, kinetic friction is more appropriate. F This tire will accelerate to the right because of the force of friction applied by the road.
Rolling Friction If the car moves along at constant velocity, ideally no forces are needed to accelerate it. However, real tires deform, and the road and tire must be continually peeled apart as the tire rolls. A small force is needed to overcome the rolling friction to keep the car moving with constant velocity. F rolling Friction This tire will slow down if no other force is applied because rolling friction opposes the motion.
Mini-lab- Friction What factors affect the amount of the frictional force between two surfaces? Using a force sensor and blocks of wood, investigate your answers to the above question. Every group should investigate the relationship between normal force and friction, and at least one other factor.
Lab Results Friction generally doesn’t depend on the surface area between two objects. Objects with less surface area have more normal force / unit area. Friction depends directly on the normal force between two objects. The types of surfaces in contact make a difference in friction observed.
Kinetic Friction and the Normal Force The force of kinetic friction is given by the formula F N is the normal force between the surfaces. μ K is the coefficient of kinetic friction, which depends on the nature of the surfaces in contact. FNFN FkFk FgFg
Maximum Force of Static Friction The maximum force of static friction is given by μ s depends on the surfaces in contact. It is usually larger than the corresponding μ k. FNFN FsFs FgFg F App
Kinetic Friction Example: Eins, Zwei, Soffa A bartender slides a 0.45 kg beer stein horizontally along a bar with an initial speed of 3.5 m/s. (The stein contains root beer of course!) The stein comes to rest near the customer after sliding 2.8 meters. Find the coefficient of kinetic friction.
Static Friction Example: Limiting Angle of Repose
FNFN F g = mg FSFS
Practice Problems: Friction OpenStax College Physics textbook, “Friction”, Exercises 5 and 6. OpenStax College Physics textbook, “Friction”, Exercises 5 and 6.
Practice Problems: Friction P. 153, #37,44
Drag Forces Part 3
Drag Forces Source: Wikipedia commons, “B-52 landing with drogue chute”
What factors influence drag? Shape of the object. Cars and planes are given aerodynamic shape to reduce drag. Properties of the fluid. Denser fluids increase drag. Speed of the object relative to the fluid. The simplest case is when F d is proportional to v.
Terminal Speed Because the drag force increases with increasing speed, a falling object will reach a speed where the drag force balances the force of gravity. This speed is called terminal speed.
Terminal Speed At terminal speed
Inclined Planes with Friction
Practice 4D, #3 A 75 kg box slides down a 25.0 o ramp with an acceleration of 3.60 m/s 2. Find k between the box and the ramp.
Givens, Unknowns and Models m = 75 kg = 25 o a x = m/s 2 k = ? Constant force in x direction, equilibrium in y. mg mg cos( ) mg sin( ) FkFk FNFN
Method Use x equation to find F k. Use y equation to find F N. Use F k and F N to find mg mg cos( ) mg sin( ) FkFk FnFn
Homework 4c: A 3.00 kg block starts from rest at the top of a 30.0 o incline and accelerates uniformly down the incline, moving 2.00 m in 1.50 s. What is the magnitude of the acceleration of the block? What is the coefficient of kinetic friction? What is the frictional force acting on the block? What is the speed of the block at the end?
Givens, Unknown and Model m = 3.00 kg = 30.0 o x = m v i = 0 t = 1.50 s a x = ? F k = ? v f = ? Equilibrium in y, acceleration in x. mg mg cos( ) mg sin( ) FKFK FnFn
Practice 4D, #1 A student moves a box of books down the hall by pulling on a rope attached to the box. The student pulls with a force of 185 N at and angle of 25.0 o above the horizontal. The box has a mass of 35.0 kg, and μ K between the box and the floor is Find the acceleration of the box.
Identify G.U.M. m= 35 kg = 25 o F app = 185 N K = 0.27 a x = ? Fapp FNFN FKFK FgFg Y- direction- Equilibrium X-direction- Constant Force
Method F app FNFN FgFg FKFK
Method Fapp FNFN FgFg FKFK
Evaluate the solution. Our answer is about 1/3 of g. This is a reasonable acceleration for an object to have over a short period of time.
Chapter Review, # 39 A 4.00 kg block is pushed along the ceiling with a constant applied force of 85.0 N that acts at an angle of 55.0 o with the horizontal. The block accelerates to the right at 6.00 m/s 2. Determine the coefficient of kinetic friction between the block and the ceiling.
G.U.M. Note that both F N and F g point down. F app = 85 N m = 4.00 kg = 55 o a=6 m/s 2 K = ? Accelerates in x, equilibrium in y. FgFg FNFN Fapp FKFK