E G H M N o R S U V measurement of kinetic friction coefficient from motion started by small perturbation Note 1 : excel trig functions assume angle is in radians. angle in radians = (angle in degrees)*pi()/180 smallest angle at kinetic quantity which block angle in friction description mass slides radians coefficient symbol "mu" formula 0 u * pi()/180 tan(0 UR) Note 2: The difference in heights, the distance travelled, and the angle of the incline are not independent quantities. Therefore, the lower height is calculated from the distance, d, travelled Note 3: The mass algebraically cancels in column T since numerator and units kg degree pure number | pure number 0.2392 12.75 by block along the incline, the angle, and the higher position. denominator are proportional to M, therefore it makes sense to look at average of u, computed for different masses 0.3392 13 0.4392 12.5 Laverage 10 work by friction average of kinetic time at gravitational total velocity velocity gravitation tota force distance kinetic friction friction angle angle of higher potential mechanical at higher | at lower al potential mechanical coefficient quantity of between computed coefficient ramp in height at height at photogat time at lower kinetic energy energy at energy at kinetic energy energy at energy at from computed from computed from 11 photogat | photogat | photogate | higher percent difference description ramp lower radians mass flag length at higher photogate higher higher at lower lower e higher mechanical photogate photogate | photogate energy 12 photogate energy symbol 0 "theta"|0 R M t 1 t 2 d photogate photogate between kinetic fri v 1 photogate v 1 photogate energy loss conservation y 2 K 1 U 1 E 1 conservation K 2 coefficient calculation U 2 E 2 WE H "mu" u "mu" 13 formula 0*pi() /180 y 1 % difference of L/t 1 L/t 2 W_F / 14 units d*sin(0 R) (1/2)M*(v 1)^2 M*gy 1 seconds seconds K 1 +U 1 (1/2)M (v 2)2 M*gy 2 tan(0_HR) and degrees pure number kilograms meters K2+U2 62- E 1 (M*g* cos(0 R)*d) 15 m/s m/s meters 15.0 meters meters Joules 0.030 Joules Joules column T 0.2392 0.2020 Joules 0.0715 Joules Joules 16 0.180 Joules 0.136 pure number pure number percent 15.0 .3392 0.030 0.1966 17 0.0672 15.0 0.180 .136 trial .4392 0.030 0.2057 0.0683 18 0.180 .136 19 18.5 .2392 0.030 0.1008 20 0.0465 18.5 0.180 0.160 .3392 0.030 .1120 .0512 21 trial 2 18.5 0.180 0.160 4392 0.030 0.0974 0.0464 0.180 22 0.160 23