Ch 05: Friction, Inclines, SystemsWorksheetSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Concept #1: Intro to Incline Plane with Friction

Concept #2: Incline with Friction & Critical Angle

Example #1: Incline with Friction

Example #2: Incline with Friction

Practice: A 5 kg block reaches the bottom of a long inclined plane with 20 m/s. The incline makes 53° with the horizontal, and the block-incline coefficient of friction is 0.4. What total time does it take the block to go up and back down?

Practice: A 10 kg block is pushed against an inclined plane with a force F that is perpendicular to the plane, as shown. The incline makes an angle of 53° with the horizontal, and the coefficients of friction between the block and the incline are 0.5 and 0.6. What minimum force F is needed to keep the block from sliding down the incline?

Additional Problems
Consider the arrangement shown in the figure. A box of mass m = 5.00 kg is pushed up a slope of inclination angle θ = 25° by an applied force Fapp. The coefficients of static and kinetic friction between the box and the inclined plane are μs = 0.30 and μk = 0.20 respectively. Make a force diagram showing all the forces acting on the box. Your diagram should have four forces in it. With the help of your diagram, determine the magnitude of the normal force acting on the box.
Consider the arrangement shown in the figure. A box of mass m = 5.00 kg is pushed up a slope of inclination angle θ = 25° by an applied force Fapp. The coefficients of static and kinetic friction between the box and the inclined plane are μs = 0.30 and μk = 0.20 respectively. Suppose the applied force has magnitude Fapp = F1 = 26.0 N. With the help of your diagram, determine the static frictional force acting on the box, assuming that the given applied force is not enough to start the box moving. 
Consider the arrangement shown in the figure. A box of mass m = 5.00 kg is pushed up a slope of inclination angle θ = 25° by an applied force Fapp. The coefficients of static and kinetic friction between the box and the inclined plane are μs = 0.30 and μk = 0.20 respectively. Calculate the maximum static frictional force that can exist between the box and the inclined plane. Note that your result should be larger than your answer to part b. Using your result for the maximum static frictional force, determine the minimum Fapp required to get the box moving.
Consider the arrangement shown in the figure. A box of mass m = 5.00 kg is pushed up a slope of inclination angle θ = 25° by an applied force Fapp. The coefficients of static and kinetic friction between the box and the inclined plane are μs = 0.30 and μk = 0.20 respectively. Suppose now that Fapp is increased to the value Fapp = F2 = 40.0 N. Calculate the resulting acceleration of the box up the plane.
A box is at rest on a variable incline with μs = 0.4 and μk = 0.3. If the box has a mass of 2 kg, what is the maximum incline angle of the slope so that the box doesn't slide down? A) 23.6° B) 66.4° C) 21.8° D) 16.7°  
A 5.00 kg block is pulled up an incline that is inclined at 36.9° above the horizontal by a horizontal force F = 90.0 N. The coefficient of kinetic friction between the block and the surface of the incline is μk = 0.20. If the block starts from rest at the bottom of the incline, how long does it take the block to travel 14.0 m to the top of the incline? 
A box on a sled slides down a long, snow-overed slope. The hill slopes at a constant angle θ. There is a small coefficient of kinetic friction of 0.16. Find an expression for the acceleration.
A 25-kg picnic cooler falls off the bed of a flatbed truck on the entrance ramp of the PG5 garage and proceeds to slide down the ramp at a constant speed. Architectural drawings of the garage show that the ramp is inclined at an angle of θ. Draw the appropriate freebody diagram and then find an algebraic expression for the coefficient of kinetic friction. Simplify the result as much as possible.
A book is at rest on an incline as shown below. A hand, in contact with the top of the book, produces a constant force Fhand vertically downward. The following figures show several attempts at drawing free-body diagrams for the book. Which figure has the correct directions for each force? The magnitudes of the forces are not necessarily drawn to scale.
A box on sled slides down a long, snow-overed slope. The hill slopes at a constant angle θ. There is a small coefficient of kinetic friction of 0.19. Find an expression for the acceleration.
The suspended 2.8 kg mass on the right is moving up, the 2 kg mass slides down the ramp, and the suspended 8 kg mass on the left is moving down. There is friction between the block and the ramp. The acceleration of gravity is 9.8 m/s2. The pulleys are massless and frictionless. What is the tension in the cord connected to the 8 kg block? 1. 42.5958 2. 33.0193 3. 45.1758 4. 39.8194 5. 46.3585 6. 36.7226 7. 43.7416 8. 35.4743 9. 38.1757 10. 42.0574
A box sits on a ramp with an adjustable inclination angle that is slowly increased. Just as the angle reaches 36°, the box begins to slide. What is the coefficient of static friction between the box and the ramp?A) 0.58B) 0.65C) 0.73D) 0.81E) It depends on the mass of the box.
A 5.00 kg block is pulled up an incline that is inclined at 36.9° above the horizontal by a horizontal force F = 90.0 N. The coefficient of kinetic friction between the block and the surface of the incline is μk = 0.20. What is the magnitude of the friction force on the block?
A mass M is initially held at rest at the top of an incline of length L, with slope forming an angle α with the horizontal (see figure). When the mass is released, it starts sliding down the incline. The coefficient of kinetic friction between the mass and the incline is μk.a) Draw a free body diagram for the mass.b) Find the acceleration of the mass.c) Find the time it take the mass to reach the bottom of the incline.Write your results in terms of M, L, α, μk, and g. Check the units/dimensions for each answer.