1. Dr. Jie Zou PHY 1151 Department of Physics1 Chapter 6 Application of Newton’s Laws

2. Dr. Jie Zou PHY 1151 Department of Physics2 Outline Frictional Forces Kinetic friction Static friction Strings and Tension Connected objects Springs and Hooke’s Law for Spring Forces Circular Motion

3. Dr. Jie Zou PHY 1151 Department of Physics3 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

4. Dr. Jie Zou PHY 1151 Department of Physics4 Kinetic Friction Kinetic friction f k : The friction encountered when surfaces slide against one another with a finite relative speed. Direction of the force of kinetic friction: Kinetic friction f k 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 f k =  k N. The constant of proportionality,  k, is referred to as the coefficient of kinetic friction.

5. Dr. Jie Zou PHY 1151 Department of Physics5 Kinetic Friction: Example 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?

6. Dr. Jie Zou PHY 1151 Department of Physics6 Kinetic Friction: Example 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?

7. Dr. Jie Zou PHY 1151 Department of Physics7 Static Friction Static friction f s : 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, f s,max. f s,max =  s N. The constant of proportionality is called  s, the coefficient of static friction. Magnitude: The force of static friction, f s, can have any value between zero and f s,max. Direction: The direction of f s is parallel to the surface of contact, and opposite to the direction the object would move if there were no friction.

8. Dr. Jie Zou PHY 1151 Department of Physics8 Static Friction: Example 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.

9. Dr. Jie Zou PHY 1151 Department of Physics9 Strings and Tension: Example 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.

10. Dr. Jie Zou PHY 1151 Department of Physics10 Springs and Hooke’s Law (Ideal) 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: Opposite to the displacement from the equilibrium length of the spring. Hooke’s Law: F = - k x. k: Force constant of the spring, units: N/m. x: displacement from the equilibrium length of the spring

11. Dr. Jie Zou PHY 1151 Department of Physics11 Springs and Hooke’s Law: Example 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?

12. Dr. Jie Zou PHY 1151 Department of Physics12 Connected Objects A block of mass m 1 slides on a frictionless tabletop. It is connected to a string that passes over a pulley and suspends a mass m 2. Find (a) the acceleration of the masses and (b) the tension in the string.

13. Dr. Jie Zou PHY 1151 Department of Physics13 Circular Motion Centripetal acceleration, a cp : Direction: Directed toward the center of the circle Magnitude: a cp = v 2 /r, where v = speed and r = radius Newton’s 2 nd Law applied to circular motion: The centripetal force is proportional to the centripetal acceleration. f cp = ma cp Centripetal force, f cp : Direction: Directed toward the center of the circle Magnitude: f cp = ma cp = mv 2 /r To make an object move in a circle with constant speed, a force must act on it that is directed toward the center of the circle.

14. Dr. Jie Zou PHY 1151 Department of Physics14 Circular Motion: Example A 1200-kg car rounds a corner of radius r = 45 m. If the coefficient of static friction between the tires and the road is  s = 0.82, what is the greatest speed the car can have in the corner without skidding?

15. Dr. Jie Zou PHY 1151 Department of Physics15 Homework See online homework assignment at www.masteringphysics.com www.masteringphysics.com Hand-written homework assignment: Chapter 6, Page 178, Problems: #10