What do we want to do today?! Thursday: 24-1-1440 A bit of housekeeping Conclude chapter-6 Introduce chapter-7 Prof. Zain Yamani Office: 15-3100/ 3102; Phone: 860-4363; Mobile: 0504608515 E-Mail: zhyamani@kfupm.edu.sa; HP: http://faculty.kfupm.edu.sa/phys/zhyamani

A bit of housekeeping Attendance If you come late, please make me aware during the (end of) the same lecture.

A bit of housekeeping I need to be in Teaching Hospital this morning. I can not attend my Office Hours, today 

Chapter-6: Applications of Newton’s Laws Friction Drag force Uniform Circular Motion

Uniform Circular Motion The centripetal force = m (v2/R) Car speeding on a flat/ horizontal track Car speeding on an inclined track Loop the loop Loss of sense of direction

A car moves on a curved, unbanked highway as shown in the figure A car moves on a curved, unbanked highway as shown in the figure. The radius of curvature of the highway is 100 m. What is the maximum speed of the car if it is not to skid ? (coefficient of static friction between the tires and the road = 0.50) 69.3 m/s 9.11 m/s 41.0 m/s 22.1 m/s 4.01 m/s 842-1

A car moves on a curved, unbanked highway as shown in the figure A car moves on a curved, unbanked highway as shown in the figure. The radius of curvature of the highway is 100 m. What is the maximum speed of the car if it is not to skid ? (coefficient of static friction between the tires and the road = 0.50) 69.3 m/s 9.11 m/s 41.0 m/s 22.1 m/s 4.01 m/s 842-1

Find the tension in the string. A 0.5 kg stone is tied to the end of a string of length 0.25 m and is rotated in a horizontal plane at a constant rate of 1.5 rev/s. The string makes an angle beta with the vertical (see figure). Find the tension in the string. 4.04 N 48.2 N 11.1 N 29.9 N 7.11 N 842-1

Find the tension in the string. A 0.5 kg stone is tied to the end of a string of length 0.25 m and is rotated in a horizontal plane at a constant rate of 1.5 rev/s. The string makes an angle beta with the vertical (see figure). Find the tension in the string. 4.04 N 48.2 N 11.1 N 29.9 N 7.11 N 842-1

© 2014 John Wiley & Sons, Inc. All rights reserved. 6-3 Uniform Circular Motion © 2014 John Wiley & Sons, Inc. All rights reserved. 10

© 2014 John Wiley & Sons, Inc. All rights reserved. 6-3 Uniform Circular Motion Answer: (a) accel downward, FN upward (b) accel upward, FN upward (c) the magnitudes must be equal for the motion to be uniform (d) FN is greater in (b) than in (a) © 2014 John Wiley & Sons, Inc. All rights reserved. 11

Car speeding on an inclined track

© 2014 John Wiley & Sons, Inc. All rights reserved. 6-3 Uniform Circular Motion Example Car in a banked circular turn: Sum components along the radial direction: Sum components along the vertical direction: Divide and replace (sin θ)/(cos θ) with tangent. Figure 6-11 Eq. (6-23) Eq. (6-24) © 2014 John Wiley & Sons, Inc. All rights reserved. 13

Challenge: add friction!!  A racing car speeds on a circular (radius: R) track that is banked at angle (q) with the horizontal. The car mass is (m) and the coefficient of static friction between car and track is m. Draw a schematic of the problem. Calculate the maximum speed that the car can run without skidding off. In what ways can this “maximum” speed be improved? As always, Legible handwriting No broadcasting

Loop the loop

© 2014 John Wiley & Sons, Inc. All rights reserved. 6-3 Uniform Circular Motion Example Bicycle going around a vertical loop: At the top of the loop we have: Solve for v and plug in our known values, including FN = 0 for the minimum answer: Figure 6-9 Eq. (6-19) © 2014 John Wiley & Sons, Inc. All rights reserved. 16

Loss of sense of direction during military air maneuvers

Chapter-6 slides 

Chapter-7: Energy Kinetic Energy Work Work done by Weight (gravity) Work done by Spring Power

Chapter-7 slides 

Mathematica can choose 

!!Check official Phys-101 website!!

Have you ever used Mathematica?

Chapter-9 A 4.0 kg block sliding on a frictionless surface breaks into two parts of equal masses. One part moves with a velocity of 3.0 m/s, due north, and the other part moves with a velocity of 5.0 m/s, 30° north of east. What was the initial sliding speed of the block? (Ignore air resistance) A) 3.5 m/s B) 2.2 m/s C) 1.9 m/s D) 4.2 m/s E) 5.1 m/s 141-F

Chapter-7 A 5.00 kg block moves in a straight line on a horizontal frictionless surface under the influence of a single force that varies with position x as shown in the Figure. If the block has a speed v = 3.00 m/s at x = 0.00 m, find the speed of the block at x = 8.00 m. A) 4.36 m/s B) 2.16 m/s C) 3.62 m/s D) 7.73 m/s E) 9.55 m/s 141-F

A rope exerts a force F on on a 20 A rope exerts a force F on on a 20.0 kg crate in lifting it vertically upward above the floor. The crate starts from rest and accelerates upward at 5.00 m/s2. How much work was done by the force F in raising the crate 4.00 m above the floor? A) 1.18 kJ B) 1.98 kJ C) 2.50 kJ D) 1.71 kJ E) 0.704 kJ 101-2

A 0.50 kg object, moving along the x-axis, experiences the force shown in Figure 1. The object’s velocity at x = 0.0 m is v = 2.0 m/s, and at x = 4.0 m is v = 8.0 m/s. What is Fmax? A) 5.0 N B) 7.2 N C) 9.7 N D) 3.2 N E) 1.8 N 101-2

A constant tension force is used to pull a 50 A constant tension force is used to pull a 50.0 kg box up a frictionless plane inclined at 30.0° relative to the horizontal. The tension force is parallel to the incline. The box is moved a distance of 30.0 m along the incline with a constant speed of 1.00 m/s. At what rate is work done by the tension force? A) 245 W B) 49.3 W C) 98.0 W D) 292 W E) 495 W 101-2

A light object and a heavy object are initially sliding with equal speeds along a horizontal frictionless surface. Then, they both slide up the same frictionless incline. Which object rises to a greater height? A) They both slide to the same height. B) The heavy object, because it has greater kinetic energy C) The light object, because it has smaller kinetic energy. D) The light object, because it weighs less. E) The heavy object, because it weighs more. 101-2

A block is dropped from a high tower and is falling freely under the influence of gravity. Which one of the following statements is true? (Ignore air resistance). A) The kinetic energy increases by equal amounts over equal distances. B) As the block falls, the net work done by all of the forces acting on the block is zero joules. C) The kinetic energy of the block increases by equal amounts in equal times. D) The potential energy of the block decreases by equal amounts in equal times. E) The total energy of the block increases by equal amounts over equal distances. 141-2

Starting from rest, an elevator with a mass of 1 Starting from rest, an elevator with a mass of 1.00×103 kg moves 100 m vertically upward in 50.0 s. At what average rate does the force from the cable do work on the elevator?   A) 19.6 kW B) 11.1 kW C) 29.7 kW D) 31.3 kW E) 15.6 kW 141-2

Two balls are launched from the same spring-loaded cannon with the spring compressed the same distance each time. Ball A has a 40 kg mass and ball B has a 60 kg mass. The relation between their speeds at the instant of launch is: 141-2

Two balls are launched from the same spring-loaded cannon with the spring compressed the same distance each time. Ball A has a 40 kg mass and ball B has a 60 kg mass. The relation between their speeds at the instant of launch is: 141-2