You are working as a science consultant on the set of a large production movie about mountain climbing. The movie calls for two dramatic scenes: one is when two climbers roped together are walking on ice, and one climber slips and falls over the edge of a cliff. The other scene is the aftermath of the fall: the climber on the ice prevents the fall by grabbing onto the ice with an axe, while the fallen climber swings freely at the end of the rope. Your job is to understand the amount of tension present in the rope for each scene, in order to determine what type of rope is safe to use. You decide to simulate the situation using a frictionless track as a model for an icy surface, and a cart and a weight tied together with a string to replicate the climbing team.

1. Make a sketch of the experimental situation for the first scene. Make reasonable assumptions and label all the forces acting on the system of two climbers. Make sure to choose most appropriate coordinate system.
2. Write down all of the mathematical relations between the forces acting on the system and resulting kinematic quantities for when the climbers are stationary and moving. What is the relation between the velocities of two climb
3. Identify the known and unknown quantities in your equations. Do you have enough equations to solve for all unknown quantities? Explain.
4. Sketch a graph of velocity vs. time and acceleration vs. time for the falling motion of your climbers. Is velocity constant? Is acceleration constant? Is your over the edge climber free falling? How does climbers’ instantaneous acceleration compare with the value of the acceleration of the free fall? If you were to "release" the climber tethered to the climber on ice and an untied climber at the same time from the same height who will reach the ground first? Explain.
5. Make a sketch of the climber swinging at the end of the rope. What are the forces acting on the climber at all times? Clearly specify the direction of the forces.
6. Draw the vector of velocity of the swinging climber right before and right after it reaches the bottom of the swing. Draw the vector of the change of velocity and subsequently the direction of the vector of acceleration. Figure out the relation between the forces acting on the climber at the bottom of the swing and it’s total acceleration.
7. What is the direction of the total force acting on the swinging climber at the bottom of the swing? Is it zero? How does the direction of the acceleration you found in the previous question relate to the direction of the total force? Explain. If the total force is not zero which component is larger? What can you tell about the magnitude of the tension force at the bottom of the swing compared to the weight of the motionless climber? Explain.