Quick questions a) Automotive A car maintaining 57 mph crests a large hill as drawn above; if we treated the hill as a fraction of a circular path, the circle's radius would be 211 m. At the apex of the hill, how many g's do the passengers experience? L g b) Anvillain Wile E, Coyote drops an anvil (35 kg) off the top of a 76 m cliff. How much work does gravity do on the anvil? r N m L |-_iow fast is it going just before it misses the roadrunner and hits the ground? rn/s L If he dropped an anvil that was twice as massive, how fast would it be going just before hitting the ground? I m/s c) Springy tackle As a prank, the kicker of a football team puts a large spring behind a padded blocking dummy their teammates use to practice tackling. Assuming that static friction keeps the dummy from moving upon impact, if tiktok videos of the prank show the teammate was running 2.1 m/s, the dummy moved 0.4 m after impact, and player stats indicate the tackling player's mass is 81 kg, what is the force constant k of the spring? d) Proportional reasoning with fluids 16 L (liters) of water flow through a 2 cm diameter pipe per minute. If the pipe widened to 4 cm, what would be the ow volume in the larger end of the pipe? 7 Umin Same scenario as above: If the water is moving through the 2 cm diameter pipe at 36 cm/s, how fast is it moving through the wider pipe? r cm/s Constants & other possibly-useful information: sin(30) = cos(60) = 1/2 (for any 0) sin(450) = cos(450) = 1/ V2 = V2/2 sin (60) = cos(30) = V 3 /2 Mass of Earth: ME = 6.0x1024 kg 1 mile = 1609.34 m; 1 mile per hour = 1.61 km/hr = 0.447 m/s = 2688 furlongs per fortnight 1 atm = 1.01x10* Pa Rotational inertia formulas for common shapes: hoop or hollow cylinder: I = MR2 thin rod about center: I = (1/12) ML2 disk or solid cylinder: I = (1/2) MR2 thin rod about end: I = (1/3) ML2 uniform solid sphere: I = (2/5) MR2 point mass a distance r from axis: I = mr2