If we release a ball of mass 2kg and radius 4cm from rest at the top of the ramp as shown: (a) What is its velocity when it reaches the bottom? (b) How many revolutions has it turned when it reaches the bottom? (c) What is its total kinetic energy, in Joules, when it reaches the bottom? 15m 30°

A recently patented pile driver pounds piles into the ground by launching 15 kg bowling balls from a spring loaded gun, up around a frictionless loop-de-loop of radius r= 8 m, and down onto the pile. When the spring is compressed by As = 2 m, the bowling balls have a speed of 20 m/s at the top of the loop, as shown. (You may v = 20 m/s r=8 m assume g = 10 m/s².) k ? As = 2 m Find the spring constant of the gun. pile A) Zero B) 100 N/m C) 2700 N/m D) 150 N/m E) 1300 N/m O A O B O D O E

R R A mass m = 88 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius R = 15.8 m and finally a flat straight section at the same height as the center of the loop (15.8 m off the ground). Since the mass would not make it around the loop if released from the height of the top of the loop (do you know why?) it must be released above the top of the loop-the-loop height. (Assume the mass never leaves the smooth track at any point on its path.) 1) What is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track? m/s Submit 2) What height above the ground must the mass begin to make it around the loop-the-loop? m Submit 3) If the mass has just enough speed to make around the loop without leaving the track, what will its speed be at the bottom of the loop? m/s Submit +

A car rounds a freeway exit turn of radius 40m at constant speed of 20m/s. The turn goes 3/4 around(not a full circle). How much work is done by the friction force on the car’s tires that allows it to turn?