Cannon Mass : Me Marble B k Mass=mm 00 mar Note: Figure not drawn to scale. Students launch identical marbles of mass mm horizontally from a toy cannon of varying mass My. where MC is always greater than mm. as shown above. The students can attach weights to the cannon to change Mb. Each time a marble is launched, the cannon slides backward before coming to rest. The coefficient of kinetic friction between the cannon and the ground is 3.: (mu). For each launch. the students vary the mass of the cannon and launch a marble with the same speed :1 relative to the ground. The students record the distance .1: that the cannon slides backward. (a) Without manipulating equations, explain how the distance 1: that the cannon slides backward changes if at all, when marbles are launched from more massive cannons. mfnlf (b) Students nd the following equation on the Internet to describe the distance :1: that the cannon slides backward. at : . Whether or not the equation is correct. is it consistent with your prediction in 'nger. part (a)? Brieyjustify your answer. (c) If constant horizontal forces were exerted over the same distance on the cannon and on the marble afterthe launch, which object would require a force with a greater magnitude to completely stop it? Without manipulating or referencing equations, briey explain your reasoning Bo (d) Students correctly derive the following equation relating the force F exerted on an object initially at rest over a distance do the mass m of the object. and the final momentum p of the object: F = 2W1. Is this equation consistent with your description in part (c)? Justify your answer. Students then discuss the mechanical energy of the marble after it has been launched by the cannon but before it reaches the ground. Both students agree that air resistance is negligible and make the following claims. Student 1: The mechanical energy ofthe marble is constant. There are no external forces exerted on the marble. so its energy does not change. Student 2: The mechanical energy decreases as the marble falls This happens because the gravitational force is doing work on the marble. (e) Which underlined phrase or phrases in student 1's statement are correct if either? If neither phrase is correct, write "none." (f) Which underlined phrase or phrases in student 1's statement are incorrect. if either? If neither phrase is incorrect: write "none." (9) Which underlined phrase or phrases in student 2's statement are correct: if either? If neither phrase is correct: write "none." (h) Which underlined phrase or phrases in student 23 statement are incorrect, if either? If neither phrase is incorrect write "none." l__ -l- fr 1 Marble Bot Horizontal Velocity Cannon Time The graph above shows the horizontal component of the velocity of the marble {dashed line) and the cannon {solid line) relative to the ground. Before time t. the marble-cannon system is at rest At time 151 the marble begins accelerating within the cannon. and at time t; the marble leaves the cannon (i) Describe the motion of the center of mass of the marble-cannon system during the time interval from if. to rig. Explain your reasoning