# Friction & Inclined Planes

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Friction & Inclined Planes
AP Physics

TWO types of Friction Static – Friction that keeps an object at rest and prevents it from moving Kinetic – Friction that acts during motion

Force of Friction The Force of Friction is directly related to the Force Normal. Mostly due to the fact that BOTH are surface forces The coefficient of friction is a unitless constant that is specific to the material type and usually less than one. Note: Does friction depend on surface area? Discuss.

Some Common Coefficients of Friction

The Key to Force Problems
Draw an accurate, labeled FBD Ask if the system is in equilibrium (∑F = 0 ) or accelerating Identify the required unknown Set up your equations, minding signs Solve for the required unknown NOW plug in values and evaluate. Check units and check for reality

Coefficient of Friction Calculation
A 24-kg crate initially at rest on a horizontal floor requires a 75 N horizontal force to set it in motion. Find the coefficient of static friction between the crate and the floor. A: Given Fs, max = 75 N m = 24 kg Unknown: μs = ? Solve: μs = Fs, max Fn μs = Fs, max mg = (75N)/(24 kg*9.8 m/s2) = (note: dimensionless)

Friction & Newton’s First Law
If the coefficient of kinetic friction between a 35-kg crate and the floor is 0.30, what horizontal force is required to move the crate to the right at a constant speed across the floor? Fn Fa Ff mg 102.9 N

Friction & Newton’s Second Law
Suppose the same 35 kg crate was not moving at a constant speed, but rather accelerating at 0.70 m/s/s. Calculate the applied force. The coefficient of kinetic friction is still 0.30. Fa= - Ff Fn Fa Ff mg 127.4 N

Warm Up: FBD Practice You take the elevator to the fourth floor.
What forces are acting on you while in the elevator?

Warm Up: FBD Practice 2 You push two boxes down the hall over a rough floor. What forces are acting on box B?

Warm Up: FBD Practice 3 Box B accelerates constantly to the right while box A sits on top of it. What forces are acting on box A?

Stranger Than Friction
Students in an introductory physics lab design an experiment to determine the coefficient of static friction between a 1.8 kg jack-o-lantern and the tabletop on which it rests. Their setup is that they attach a massless string to the jack-o-lantern, loop it over a pulley, and then attach the other end to a pail in which the students will add sand as the experiment progresses. The pail with sand was observed to weigh 11 N when the jack-o-lantern began to slide. A. Draw a free body diagram for this set up. B. What is known? What are you solving for? What equations can you use? C. Find the coefficient of static friction.

Stranger Than Friction Continued
Key to solving: The maximum force of static friction is equal to the force exerted by the pail at the moment the jack-o-lantern begins to slide. Fs, max= μsN μs = Fs, max = W N mg After substituting values….. μs = 0.61 Reality Check: Coefficients of friction are always between 0 and about 1 and are dimensionless

Static and Kinetic Friction Lab
Today: 1. Collect data 2. Analysis questions 1-3 Tomorrow: 1. Graphical analysis 2. Conclusions

Inclines q q Ff FN q q q Tips Rotate Axis Break weight into components
Write equations of motion or equilibrium Solve mg q

Friction & Inclines A person pushes a 30-kg shopping cart up a 10 degree incline with a force of 85 N. Calculate the coefficient of friction if the cart is pushed at a constant speed. Fa Fn q Ff mg 0.117 q

Example A 5-kg block sits on a 30 degree incline. It is attached to string that is thread over a pulley mounted at the top of the incline. A 7.5-kg block hangs from the string. a) Calculate the tension in the string if the acceleration of the system is 1.2 m/s/s b) Calculate the coefficient of kinetic friction. T FN m2 m2gcos30 Ff 30 T m2g m1 30 m2gsin30 m1g

Example 64.5 N 0.80 N

10/4/13 Exit Ticket On a half sheet of paper:
Explain why pushing downward on a book as you push it across a table increases the force of friction between the table and the book. (Use vocabulary from this unit to answer this question!)