In june 1997 the near spacecraft, on its way to photograph the asteroid eros, passed near the asteroid mathilde. from photos transmitted by the spacecraft, mathilde's size was known. it is presumably made of rock. rocks on earth have a density of about 3000 kg/m3 (3 grams/cm2). from the observations of the motion of the spacecraft as it passed mathilde, scientists were able to learn something surprising about the asteroid in this problem you will analyze a similar situation. a spacecraft with mass 900 kg was traveling at nearly constant velocity with speed 9000 m/s. it flew past an asteroid, and the distance of closest approach (d in the diagram) was 3700 km (3.7e6 m). from photos taken by the spacecraft, it was determined that the asteroid had roughly the shape of a box 40 km by 60 km by 20 km (4e4 m by 6e4 m by 2e4 m)

Amass m = 74 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius r = 18.4 m and finally a flat straight section at the same height as the center of the loop (18.4 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? 2. what height above the ground must the mass begin to make it around the loop-the-loop? 3. if the mass has just enough speed to make it around the loop without leaving the track, what will its speed be at the bottom of the loop? 4. if the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the final flat level (18.4 m off the ground)? 5. now a spring with spring constant k = 15600 n/m is used on the final flat surface to stop the mass. how far does the spring compress?