LECTURE 16: Friction

Transcription

1 Lectures Page 1 LECTURE 16: Friction Select LEARNING OBJECTIVES: i. ii. iii. iv. v. vi. vii. viii. ix. x. xi. Identify the direction that friction is acting. Identify which object(s) are creating a force of friction. Determine which normal force is associated with a particular force of friction. Decide if friction is static or kinetic. Determine if static friction is equal to or less than the maximum static friction. Friction max is only equal to the coefficient of static friction times the normal force when the static friction is greatest it can be without slipping. Otherwise it is equal to whatever is required to keep the surfaces from slipping. Know when static or kinetic friction is to be use Understand and interpret a force of friction vs time graph. Identify key features such as F fs,max, and regions of relative motion or no relative motion. Understand that our definition of F fs,max =μs F N and F fk =μk F N are empirical expressions. Demonstrate the ability to decide if friction can be ignored in certain scenarios where the force of friction is negligible. Further develop (or introduce?) the concept of relative motion. TEXTBOOK CHAPTERS: Giancoli (Physics Principles with Applications 7 th ) :: 4-8 Knight (College Physics : A strategic approach 3 rd ) :: 5.5 BoxSand :: Forces ( Friction ) WARM UP: Discuss the validity of this statement: We rotate the coordinate system when working with inclined planes because coordinate systems should be parallel or perpendicular to a surface. Now that we have seen objects sliding across frictionless horizontal and inclined surfaces, we will add some more complexity/reality to these scenarios with the addition of friction. Previously we have considered the force of gravity, normal forces, tension, and generic applied/push forces. We now add friction to our inventory of forces that we use. Friction Recall that forces are the descriptions we give to underlying interactions between objects. The fundamental interaction responsible for friction is the electromagnetic interactions between charged

2 Lectures Page 2 particles at the surfaces of two objects on contact. This electromagnetic interaction is the very same that is responsible for the normal force discussed previously. Recall, the underlying interaction is a non-contact interaction, but we call both the normal force and friction contact forces because at the macroscopic level the interactions are only noticeable when it looks like the objects are physically touching. Friction can occur between two solid objects on contact, a solid object and a fluid, or between two fluids on contact. The force of friction related to fluids is labeled as the viscous force. In this course we will only consider frictional forces between two solid objects. The interactions between the charged particles between two surfaces on contact are complicated. On the microscopic level, you can imagine the large numbers of particles interacting with one another make it hard to fundamentally come up with a model to describe the results of these interactions. However, on the macroscopic level, empirical observations led to a set of simple proportionalities which we will use when working with friction. Through careful experiments, it was shown that the force of friction is proportional the normal force between the two objects in contact. This is mathematically written as PRACTICE: If the normal force between two surfaces in contact increases by a factor of 2, how does the frictional force change? PRACTICE: If the surface area between two surfaces in contact increases by a factor of 2, how does the frictional force change? Perhaps even more interesting, the proportionally constant between the same two surfaces (e.g. rubber and concrete) is different depending if the surfaces are sliding relative to one another. You might already have experience with this observation. If you have ever pushed a box across a floor, you may have noticed it was harder to get the box to move than it was to keep the box moving. Because of this difference in observed behavior, we split friction up into two case specific forces: kinetic friction, and static friction. Kinetic friction When two surfaces are in contact with one another, and are moving relative to each other then we say that there is kinetic friction between the two surfaces. The direction of this friction will always be parallel to the two surfaces in contact, and in a direction that opposes the relative direction of motion between the two surfaces. Do not confuse direction of motion and relative direction of motion. For example, consider a box in the back of a pickup truck as shown below

3 Lectures Page 3 Now if the truck accelerates with a large enough magnitude, the box might not stay in place, it will slide across the bed of the truck. What direction is the kinetic friction while the box is sliding? From an outside observer's perspective, the box looks like it is moving to the right, so by applying the definition that friction oppose direction of motion, the observer would say the kinetic friction is to the left. This is incorrect! We need to consider the relative motion between the box and the bed of the truck. Both the box and the bed of the truck are accelerating to the right, however, the truck bed itself is accelerating to the right with a larger magnitude than the box is. Thus the box looks like it is moving left relative to the truck bed, and the kinetic friction force is to the right on the box. This is shown in the figure below. *What direction is the kinetic friction on the bed of the truck, and how does it's magnitude compare to the magnitude of kinetic friction on the box? Recall the magnitude of frictional forces is proportional to the normal force between the two surfaces in contact. For kinetic friction, we call the proportionality constant "the coefficient of kinetic friction", and use the symbol µ k. Thus the magnitude for kinetic friction is mathematically written as: And this is read as "the force of kinetic friction from surface 1 on object 2 is equal to the coefficient of kinetic friction times the normal force from surface 1 on object 2". Notice how our definition for the magnitude of kinetic friction is not dependent on the speed of which the object moves relative to the surface? Remember, this definition was made by empirical observation, and to a very good approximation the magnitude of the kinetic friction was not seen to depend on speed.

4 Lectures Page 4 PRACTICE: A box slides down an incline with an acceleration of 2 m/s 2. If the angle of the incline with respect to the horizontal is 30 degrees, what is the coefficient of kinetic friction between the box and the incline? Static friction When two surfaces are in contact with one another, and are not moving relative to each other then we say that there is static friction between the two surfaces. The direction of this friction will always be parallel to the two surfaces in contact, and in a direction that opposes the desired relative direction of motion between the two surfaces. Do not confuse direction of motion and desired relative direction of motion. What do I mean by "desired" relative motion? Static friction helps an object stay in place relative to the surface it is in contact with. To determine the direction of static friction, we often do a thought experiment where we ask the question, "what direction would the object move if there was no friction between the surfaces". This direction is the "desired" direction of the object, however static friction opposes that direction, keeping the object in place. Finding the direction of static friction is not a trivial task, and is best learned by practice. Let's consider a box on a horizontal surface. If we begin to push the box, the box doesn't move. So we push a bit harder, yet the box sill doesn t move. Again, we push even harder, the box still doesn't move! Finally, at a certain magnitude of pushing force, the box starts to move relative to the contact surface, where we then observe that once moving, we don't need to push as hard for the box to continue to move relative to the surface. So it turns out, that the static friction is not constant. In fact, it self-adjusts to exactly counteract the pushing force so that the object does not move relative to the contact surface. Then there is a maximum value for which the static friction can adjust to before the object moves relative to the contact surface and the motion is then described by kinetic friction. If we plot the force of friction vs time we might get a graph similar to the one below.

5 Lectures Page 5 Some key features are labeled on the graph above. The force of static friction is labeled in blue. But notice that the maximum allowed force of static friction before the object 2 moves relative to surface 1 is labeled and referred to as "the maximum force of static friction". Thus we use the red labeled notation if we know the scenario we are analyzing is at this maximum static friction value. Also notice that once the object 2 moves relative to surface 1, the kinetic friction is a constant value less than the maximum force of static friction. Mathematically, we need to split the static friction up into two parts, one for when the object is not moving (the blue part in the graph above), and the second part for the observable moment when the object is just about ready to move relative to a contact surface (the red point in the graph above). For static friction, we call the proportionality constant, "the coefficient of static friction" and use the symbol µs. Notice how the force of static friction can take on a range of values, but we don't know it's exact magnitude until we know the maximum force of static friction. Thus the scenario for when an object is just about ready to move relative to a contact surface is an important one, it is only when we know this detail that we can use the equation for the maximum force of static friction. Otherwise, if we do not know our system is about ready to move relative to a contact surface, we cannot easily quantify the magnitude of static friction. PRACTICE: The box below is held in place against the wall with an applied force. What is the direction of static friction on the box?

6 Lectures Page 6 (1) (2) (3) (4) Towards the right. Upwards. Downwards. Not enough information. PRACTICE: What is the maximum acceleration that the bottom black can attain without the top block sliding relative to the bottom? The coefficient of static friction between the two blocks is 0.50 and the coefficient of kinetic friction is Rolling friction Give a shopping cart a light push and set it rolling across the grocery store floor. If you examine the wheels carefully, you will notice that they are not sliding relative to the ground, thus there is no kinetic friction. Also, the wheels do not have any motors attached to force rotation of the wheel, thus there is no static friction. If there is no static friction and no kinetic friction, then why does the cart eventually come to rest? There must be some sort of friction present. ( We are ignoring air resistance here. ) The friction responsible for the cart coming to rest is called rolling friction. Rolling friction is the result of many complicated features of wheels (e.g. deformation of the wheel on contact, bearings etc ). Despite the complicated nature of rolling friction we can still quantify it must like kinetic friction with the following expression:

7 Lectures Page 7 The coefficient of rolling friction, µ r, is typically very small. This is hopefully is relatable to some of your observations. It is much easier to push an object on wheels compared to sliding it across a floor. PRACTICE: Draw a free body diagram of a shopping cart as you push it across a floor at a constant speed. Conceptual questions for discussion Discuss the validity of the following statement: The coefficient of static friction for rubber is What are the SI units for the coefficient of static friction?...and the coefficient of kinetic friction?