A constant force Fis 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 uk. The dart/block system then slides across the table and comes to rest after traveling a distance D. 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. Students derive the following equation for the distance D. D= — FLn (m+M)B) Students derive the following equation for the distance D. D= — FLn (m+M)?Mx9 Without algebraic manipulation of equations C) 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.
D) Predict what will happen to the launch velocity of the dart if the length of the tube was doubled. E) Students are given an equation for the launch velocity of the block as follows. v= 1 equations explain whether this equation accurately matches your explanation in part (D).