A constant force F is exerted on a dart of mass m in the horizontal direction as it moves through a tube of length L. After exiting the tube, the dart collides with a box of mass M that sits at rest on a table with coefficient of friction μk. The dart/block system then slides across the table and comes to rest after traveling a distance D. Required:
a. Students experiment with a variety of tubes. Assuming that air resistance is negligible, and that all other parts of the experiment remain the same, should the students use a long tube, or a short tube make the stopping distance D the longest?
b. Students then change the force so that it can be described as a function of position F(x)=12x. Explain how the students could use the equation given above to find the launch speed of the dart, if the length of the tube is 2 meters.
c. Predict what will happen to the launch velocity of the dart if the length of the tube was doubled. Justify your answer.