**50. A person starts from rest at the top of a large frictionless spherical surface, and slides into the water below (see the drawing). At what angle 0 does the person leave the surface? (Hint: When the person leaves the surface, the normal force is zero.)

You and your friends pull your car off a mountain road onto an overlook to take pictures of the frozen lake below. You lose your footing on the packed snow, fall over the cliff, and land in a soft snow bank on a ledge, 10 feet below the edge. The cliff's wall is too smooth to climb upwards and too steep and dangerous to climb the remaining 300 feet to the bottom. While trying to think your way out of your predicament, you realize one reason you had slipped was that you had misjudged how the cliff sloped towards the edge (a decline of about 5-10 degrees). There is nothing near the edge to which your friends can tie a rope, and they fear the footing is too slippery for them to pull you to the top. However, they can get the car close enough to the edge to tie the rope to the bumper and hang it over the edge. You are worried, however, that the car might slip over the edge as well. On your phone (which has survived the fall) you look up the coefficient of static friction of snow tires on…

a tire swing is hanging from a rope of the length 5 meters long. It swings from an initial angle of 30 degrees relative to the vertical. The mass of the tire is 19k. what is the maximum tension

Denisse is playing a pinball machine. she notices that the 0.012 kg ball is shot from the plunger and moves into a circular path with a radius of 0.22 m. if the magnitude of the force necessary to keep the ball in the Circular path is 0.030 N, what is the speed of the steel ball?