Application of Newton’s Laws Chapter 6 Application of Newton’s Laws Dr. Jie Zou PHY 1151 Department of Physics

Dr. Jie Zou PHY 1151 Department of Physics Outline Frictional Forces Kinetic friction Static friction Strings and Tension Springs and Hooke’s Law for Spring Forces Various Examples Dr. Jie Zou PHY 1151 Department of Physics

Dr. Jie Zou PHY 1151 Department of Physics Frictional Forces The origin of friction: Even “smooth” surfaces have irregularities when viewed at the microscopic level. This type of roughness contributes to friction. Two types of friction: Kinetic friction Static friction Dr. Jie Zou PHY 1151 Department of Physics

Dr. Jie Zou PHY 1151 Department of Physics Kinetic Friction Kinetic friction fk: The friction encountered when surfaces slide against one another with a finite relative speed. Direction of the force of kinetic friction: Kinetic friction fk acts to oppose the sliding motion at the point of contact between the surfaces. Magnitude of the force of kinetic friction: In general, the force of kinetic friction is found to be proportional to the magnitude of the normal force, N, or fk = kN. The constant of proportionality, k, is referred to as the coefficient of kinetic friction. Dr. Jie Zou PHY 1151 Department of Physics

Kinetic Friction: Example 6-1 Someone at the other end of the table asks you to pass the salt. You slide the 50.0-g salt shaker in their direction, giving it an initial speed of 1.15 m/s. (a) If the shaker comes to a rest with constant acceleration in 0.840 m, what is the coefficient of kinetic friction between the shaker and the table? Dr. Jie Zou PHY 1151 Department of Physics

Kinetic Friction: Example 6-2 A trained sea lion slides from rest with constant acceleration down a 3.0-m-long ramp into a pool of water. If the ramp is inclined at an angle of 23 above the horizontal and the coefficient of kinetic friction between the sea lion and the ramp is 0.26, how long does it take for the sea lion to make a splash in the pool? Dr. Jie Zou PHY 1151 Department of Physics

Dr. Jie Zou PHY 1151 Department of Physics Static Friction Static friction fs: Static friction tends to keep two surfaces from moving relative to one another. There is an upper limit to the force that can be exerted by static friction, fs,max. fs,max = sN. The constant of proportionality is called s, the coefficient of static friction. Magnitude: The force of static friction, fs, can have any value between zero and fs,max. Direction: The direction of fs is parallel to the surface of contact, and opposite to the direction the object would move if there were no friction. Dr. Jie Zou PHY 1151 Department of Physics

Static Friction (Cont.) Dr. Jie Zou PHY 1151 Department of Physics

Static Friction: Example 6-3 A flatbed truck slowly tilts its bed upward to dispose of a 95.0-kg crate. For small angles of tilt the crate stays put, but when the tilt angle exceeds 23.3 the crate begins to slide. (a) What is the coefficient of static friction between the bed of the truck and the crate? (b) Find the magnitude of the static friction acting on the crate. Dr. Jie Zou PHY 1151 Department of Physics

Strings and Tension: Example 6-5 To hang a 6.20 kg pot of flowers, a gardener uses two wires-one attached horizontally to a wall, the other sloping at an angle of  = 40.0 and attached to the ceiling. Find the tension in each wire. Dr. Jie Zou PHY 1151 Department of Physics

Springs and Hooke’s Law Magnitude of the spring force: The spring force is proportional to the amount, x, by which it is stretched or compressed. Direction of the spring force: the force is opposite to the displacement, that is the it is restoring. Hooke’s Law: F = - k x. k: Force constant of the spring, units: N/m. Dr. Jie Zou PHY 1151 Department of Physics

Springs and Hooke’s Law: Exercise 6-1 A 1.50-kg object hangs motionless from a spring with a force constant k = 250 N/m. How far is the spring stretched from its equilibrium length? Dr. Jie Zou PHY 1151 Department of Physics

Dr. Jie Zou PHY 1151 Department of Physics Homework Chapter 6, Page 165, Problems: #1, 7, 9, 19. Dr. Jie Zou PHY 1151 Department of Physics