Newton’s Laws Applications Friction Friction is the force that opposes a sliding motion. Friction is due to microscopic irregularities in even the smoothest of surfaces. Microscopic View Big view: N Surfaces look perfectly smooth. (friction) Fpush f W Small view: Microscopic irregularities resist movement. Friction may or may not exist between two surfaces. The direction of friction, if it exists, is opposite to the direction object will slide when subjected to a horizontal force. It is always parallel to the surface. Friction Friction is the force that opposes a sliding motion. Friction is due to microscopic irregularities in even the smoothest of surfaces. Friction is highly useful. It enables us to walk and drive a car, among other things. Friction is also dissipative. That means it causes mechanical energy to be converted to heat. We’ll learn more about that later. Friction depends on the normal force. The friction that exists between two surfaces is directly proportional to the normal force. Increasing the normal force increases friction; decreasing the normal force decreases friction. This has several implications, such as… Friction on a sloping surface is less than friction on a flat surface (since the normal force is less on a slope). Increasing weight of an object increases the friction between the object and the surface it is resting on. Weighing down a car over the drive wheels increases the friction between the drive wheels and the road (which increases the car’s ability to accelerate). Static Friction This type of friction occurs between two surfaces that are not slipping relative to each other. f s s N fs : static frictional force (N) s: coefficient of static friction N: normal force (N) fs < sN is an inequality! The fact that the static friction equation is an inequality has important implications. Static friction between two surfaces is zero unless there is a force trying to make the surfaces slide on one another. Static friction can increase as the force trying to push an object increases until it reaches its maximum allowed value as defined by s. Once the maximum value of static friction has been exceeded by an applied force, the surfaces begin to slide and the friction is no longer static friction. Static friction and applied horizontal force Force Diagram N Physics surface W fs = 0 There is no static friction since there is no applied horizontal force trying to slide the book on the surface. Static friction and applied horizontal force Force Diagram N fs Physics F surface W 0 < fs < sN and fs = F Static friction is equal to the applied horizontal force, and there is no movement of the book since SF = 0. Static friction and applied horizontal force Force Diagram N fs Physics F surface W fs = sN and fs = F Static friction is at its maximum value! It is still equal to F, but if F increases any more, the book will slide. Static friction and applied horizontal force Force Diagram N fk Physics F surface W fs = sN and fs < F Static friction cannot increase any more! The book accelerates to the right. Friction becomes kinetic friction, which is usually a smaller force. Kinetic Friction This type of friction occurs between surfaces that are slipping past each other. fk = kN fk : kinetic frictional force (N) k: coefficient of kinetic friction N: normal force (N) Kinetic friction (sliding friction) is generally less than static friction (motionless friction) for most surfaces. Sample Problem A boulder of mass 45 kg is pushed on a surface with a coefficient of kinetic friction of 0.85. What force has to be applied to produce an acceleration of 0.20 m/s2? Problem The coefficient of kinetic friction for wood on wood is 0.55. What is the force of friction of a wood block of mass 3.5 kg being pulled on a wood floor? Sample Problem A brick has a mass of 1.2 kg. A force of 5.4 N is needed to move the brick along the floor with a constant velocity. What is the coefficient of friction? Static friction on a ramp Without friction, the book will slide down the ramp. If it stays in place, there is sufficient static q friction holding it there. Wx = mgsinq and N = mgcosq At maximum angle before the book slides, we can prove that s = tanq. Static friction on a ramp Assume q is maximum angle SF = 0 for which book Wx = fs stays in place. mgsinq = smgcosq s = sinq/cosq = tanq q q fs = mgsinq and N = mgcosq At maximum angle before the book slides, we can prove that s = tanq. Tension and Strings and Springs Tension Tension is a pulling force that arises when a rope, string, or other long thin material resists being pulled apart without stretching significantly. Tension always pulls away from a body attached to a rope or string and toward the center of the rope or string. A physical picture of tension Imagine tension to be the internal force preventing a rope or string from being pulled apart. Tension as such arises from the center of the rope or string. It creates an equal and opposite force on objects attached to opposite ends of the rope or string. Tension examples Note that the pulleys shown are magic! They affect the tension in any way, and serve only to bend the line of action of the force. Springs (Hooke’s Law) The magnitude of the force exerted by a spring is proportional to the amount it is stretched. F = kx F: force exerted by the spring (N) k: force constant of the spring (N/m or N/cm) x: displacement from equilibrium (unstretched and uncompressed) position (m or cm) The direction of the force is back toward the equilibrium (or unstretched) position. Sample problem A 1.50 kg object hangs motionless from a spring with a force constant of k = 250 N/m. How far is the spring stretched from its equilibrium length? Sample problem A 1.80 kg object is connected to a spring of force constant 120 N/m. How far is the spring stretched if it is used to drag the object across a floor at constant velocity? Assume the coefficient of kinetic friction is 0.60. Uniform Circular Motion An object that moves at uniform speed in a circle of constant radius is said to be in uniform circular motion. Question: Why is uniform circular motion accelerated motion? Answer: Although the speed is constant, the velocity is not constant since an object in uniform circular motion is continually changing direction. Centrifugal Force Question: What is centrifugal force? Answer: That’s easy. Centrifugal force is the force that flings an object in circular motion outward. Right? Wrong! Centrifugal force is a myth! There is no outward directed force in circular motion. To explain why this is the case, let’s review Newton’s 1st Law. Newton’s 1st Law and cars •When a car accelerates forward suddenly, you as a passenger feel as if you are flung backward. • You are in fact NOT flung backward. Your body’s inertia resists acceleration and wants to remain at rest as the car accelerates forward. •When a car brakes suddenly, you as a passenger feel as if you are flung forward. • You are NOT flung forward. Your body’s inertia resists acceleration and wants to remain at constant velocity as the car decelerates. When a car turns You feel as if you are flung to the outside. You call this apparent, but nonexistent, force “centrifugal force”. You are NOT flung to the outside. Your inertia resists the inward acceleration and your body simply wants to keep moving in straight line motion! As with all other types of acceleration, your body feels as if it is being flung in the opposite direction of the actual acceleration. The force on your body, and the resulting acceleration, actually point inward. Centripetal Acceleration Centripetal (or center-seeking) acceleration points toward the center of the circle and keeps an object moving in circular motion. This type of acceleration is at right angles to the velocity. This type of acceleration doesn’t speed up an object, or slow it down, it just turns the object. Centripetal Acceleration ac = v2/r ac: centripetal acceleration in m/s2 v: tangential speed in m/s v ac r: radius in meters Centripetal acceleration always points toward center of circle! Centripetal Force A force responsible for centripetal acceleration is referred to as a centripetal force. Fc Centripetal force is simply mass times centripetal acceleration. Fc = m ac Always toward Fc = m v2 / r Fc: centripetal force in N center of circle! v: tangential speed in m/s r: radius in meters Any force can be centripetal The name “centripetal” can be applied to any force in situations when that force is causing an object to move in a circle. You can identify the real force or combination of forces which are causing the centripetal acceleration. Any kind of force can act as a centripetal force. Static friction As a car makes a turn on a flat road, what is the real identity of the centripetal force? Tension As a weight is tied to a string and spun in a circle, what is the real identity of the centripetal force? Gravity As the moon orbits the Earth, what is the real identity of the centripetal force? Normal force with help from static friction As a racecar turns on a banked curve on a racing track, what is the real identity of the centripetal force? Gravity, with some help from the normal force When you are riding the CAROLINA COBRA at Carowinds, what is the real identity of the centripetal force when you are on a vertical loop? Sample problem A 1200-kg car rounds a corner of radius r = 45 m. If the coefficient of static friction between tires and the road is 0.93 and the coefficient of kinetic friction between tires and the road is 0.75, what is the maximum velocity the car can have without skidding?