2Homework 6: The Traffic Light A traffic light weighing 122 N hangs from a cable tied to two other cables fastened to a support, as in the figure below. The upper cables make angles of 37° and 53° with the horizontal. These upper cables are not as strong as the vertical cable and will break if the tension in them exceeds 100N.Will the traffic light remain hanging in this situation, or will one of the cables break?
3Solution of Homework 6: The Traffic Light Free-Body Diagram for the Traffic LightFree-Body Diagram for the Knot
4Solution of Homework 6: The Traffic Light Forces along the x axis:Why zero?Forces along the y axis:Why zero?Both values of T1 and T2 are less than 100 N. So, the cables will not break.
5Friction Frictional forces are unavoidable in our daily lives. If we were not able to counteract them, they would stop every moving object and bring every rotating shaft to a halt. About 20% of the gasoline used in a car is needed to counteract friction.On the other hand, if friction were totally absent, we could not get an automobile to go anywhere, and we could not walk or ride a bicycle. Nobody can hold a pencil and it would not write.Here we deal with the frictional forces that exist between dry solid surfaces, either stationary relative to each other (static) or moving across each other at slow speeds (kinetic).The friction is a passive force. When a force is applied to an object, the friction force arises against it.→fs : static frictional forcefk : kinetic frictional force→
6Friction(a)A block rests on a tabletop with the gravitational force balanced by a normal force.There is no friction force,No motion(b)(c)(d)An increasing force is applied to the block, attempting to pull it to the left.The block does not move. An equal and opposite static frictional force arises between the object and the surface, exactly balancing the applied force.
7Friction Acceleration Constant velocity (e) Eventually the object will be accelerated when the applied force reaches a certain magnitude.The frictional force that oppose the motion is now the kinetic frictional force,AccelerationConstant velocity(f)The magnitude of the kinetic frictional force, which acts when there is motion, is less than the maximum magnitude of the static frictional force, which acts when there is no motion.To move the block across the surface with a constant speed, the magnitude of the applied force must be decreased once the block begins to move,
9Two surfaces In Contact FrictionWhen two ordinary surfaces are placed together, only the high points touch each other.Some contact points do cold-welt together. These welds produce static friction when an applied force attempts to slide the surface relative to each other.If the applied force is great enough to pull one surface across the other, there is first a tearing of welds (at breakaway) and then a continuous re-forming and tearing of welds as movement occurs.If the two surfaces are pressed together harder, many more points cold-weld. Sliding the surfaces relative to each other requires a greater applied force.Two surfaces In Contact
10Properties of Friction Experiment shows that when a body presses against a surface and a force F attempts to slide the body along the surface, the resulting frictional force has three properties.Property 1If the body does not move, then the static frictional force fs and the component of F that is parallel to the surface balance each other. They are equal in magnitude, and oppose in direction.Property 2The magnitude of fs has a maximum value fs,max that is given byProperty 3If he body begins to slide along the surface, the magnitude of the frictional force rapidly decreases to a value fk given by→→→→μs : coefficient of static frictionμk : coefficient of kinetic friction
11Properties of Friction Friction depends on how strongly the surfaces are pressed together. This pressing strength is represented by the normal force FN.It is easier to keep an object sliding than to get it starts sliding.The coefficients μs and μk are dimensionless and must be determined experimentally.→The value of μs and μk depends on certain properties of both the body and the surface. Therefore, they are usually referred to with the preposition “between.”
12Properties of Friction A block lies on a floor.What is the magnitude of the frictional force on it from the floor?If a horizontal force of 5 N is now applied to the block, but the block does not move, what is the magnitude of the frictional force on it?If the maximum value of fs,max of the static fictional force on the block is 10 N, will the block move if the magnitude of the horizontally applied force is 8 N?What about if it is 12 N?What is the magnitude of the frictional force in part (c)?Zero5 NNoYes8 N
13Example: JaguarIf a car’s wheels are “locked” (kept from rolling) during emergency braking, the car slides along the road. Ripped-off bits of tire and small melted sections of road form the “skid marks.”The record for the longest skid marks on a public road was reportedly set in 1960 by a Jaguar on the M1 highway in England –the marks were 290 m long.Assuming that μk = 0.6 and the car’s acceleration was constant during the braking, how fast was the car going when the wheels became locked?
15Checkpoint→F1= 10 N is applied to a box on a floor, but the box does not slide. Then, F2 is increased from zero. Before the box begins to slide, do the following quantities increase, decrease, or stay the same?(a) The magnitude of the frictional force on the box.(b) The magnitude of the normal force on the box from the floor.(c) The maximum value fs,max of the static frictional force on the box.→The same, 10 NDecreaseDecrease
16Example: Amber BlockA 2.5 kg block is initially at rest on a horizontal surface. A horizontal force F of magnitude 6 N and a vertical force P are then applied to the block (see below). The coefficients of friction for the block and surface are μs = 0.4 and μk = 0.25.Determine the magnitude of the frictional force acting on the block if the magnitude of P is8 N (b) 10 N (c) 12 N→→→
17Example: Amber Block FN f Fg The box does not move The box moves →The box does not movef→Fg→The box movesForces along the y axis:On the verge of sliding, the maximum static frictional force is:The box moves
18Final Homework 7: Coin On A Book The figure below shows a coin of mass m at rest on a book that has been tilted at an angle θ with the horizontal. By experimenting, you find that when θ is increased to 13°, the coin is on the verge of sliding down the book, which means that even a slight increase beyond 13° produces sliding.What is the coefficient of static friction μs between the coin and the book?Hint: Draw the free-body diagram of the coin first.