First-Year Engineering Program. Physics RC Reading Module

Transcription

1 Physics RC Reading Module

2 Frictional Force: A Contact Force Friction is caused by the microscopic interactions between the two surfaces. Direction is parallel to the contact surfaces and proportional to the normal force between them. 2

3 Normal Force Normal Force: A contact force that exists between two solid objects Direction is perpendicular to the contact surfaces Rails W = mg R 3

4 Friction Friction is a process that results in a force that opposes an action. If there were NO friction, we would not be able to walk nor would items stay on a desk Energy has to be used in overcoming a frictional force. Causes unwanted losses in a system 4

5 FRICTION First-Year Engineering Friction Static Friction Kinetic Friction 5

6 Static Friction First-Year Engineering Static Friction: Acts to prevent objects from moving relative to each other A book on a table A ball on a flat surface 6

7 Static Friction First-Year Engineering To just move a body from rest, we need to apply a force just greater than the Static Frictional Force (F f ) F f = µ 0 Pulling Force W Rails Force required to just move the object is F f µ 0 : Coefficient of Static Friction= F f / 7

8 FRICTION Kinetic Friction Sliding Friction Due to sliding action of the object Rolling Friction Due to rolling action of the object 8

9 Kinetic Friction First-Year Engineering Kinetic Friction: exists between moving surfaces Generally transfers kinetic energy to heat. Moving could be sliding, rolling, or both Sliding friction is generally much larger than rolling friction (which is why you want to avoid steep sections of track) F f = µ K motion W µ k : Coefficient of Kinetic Friction Rails 9

10 Sliding vs. Rolling Friction Sliding Friction Caused due to sliding action of bodies µ S - Coefficient of Sliding friction Rolling Friction Caused due to rolling action of bodies µ R - Coefficient of Rolling friction First-Year Engineering We will calculate µ R and µ 0 in Lab 2 while calculating energy losses by Observing balls rolling on a circular arc Causing conjoined ball pairs to slide down a ramp 10

11 Slippage tan(θ c ) μ μ tan( ) R' R First-Year Engineering If section of track has a very high slope, a ball might tend to slide as it is trying to roll. This is slippage. Θ c : Angle above which some slippage of the ball occurs. 0 (Where R is the effective rolling radius and R is the ball radius, and β is angle measured in this lab) 2 You will calculate this angle in Lab 2. 11

12 Effects of a Curved Path First-Year Engineering Frictional forces are proportional to normal forces. For a curved path, we need to also consider the normal component of centripetal force, F C. V F c 12

13 Magnitude of Centripetal Force Centripetal Force F C = m V 2 / R F c V m: mass of the body in circular motion V: speed of the body R: radius of curvature From Newton s 2 nd Law: F=ma, the Centripetal Acceleration is a C = V 2 / R 13

14 Forces acting on a body in circular motion Vertical Loop V > (gr) ½ W W W W 14

15 Critical Velocities For the ball to stay on the track at the top most point of a vertical loop, its velocity at that point must be V > (gr) ½. W For the ball to not fly off the top of a bump, then you need V < (gr) ½ (based on similar reasoning). 15

16 Horizontal Loops/Curves First-Year Engineering A horizontal loop is a special case of a curve with a vertical axis. Generally, the exit is lower than the entrance. 16

17 Curved Track Banking Angles (for any curve) A bank creates the centripetal force needed to keep the ball on the track by using the ball s weight. The normal force opposing gravity will be angled toward the center of the arc. An expression for the required bank angle is (where v is speed): tan( ) 2 v g r r 17