# A spool of thread, free to unwind, is on a horizontal surface (with friction) and pulled...

###### Question: A spool of thread, free to unwind, is on a horizontal surface (with friction) and pulled directly upward (ty) a times. The spool rolls without slipping on the floor. The spool has a mass M, moment of inertia 1, and a radius of R. Assume the string is wrapped around the spool at a radius r (where r <R). 1) Which equation below is a correct expression of Newton's Second Law (XF- ma ) in the x (hortzontal) -direction for this situation. Assume all the forces below are magnitudes and that to the right is considered the positive direction. FT-Ff-Mar FT+ Mar 2) Which equation below is a correct expression of Newton's Second Law (F-ma ) in the y-direction for this situation. Assume all the forces below are magnitudes and up is considered the positive direction. FN- F&t FT-May FN- Fg- FT- May FN-F&-May 3 which equation below is a correct expression of the rotational equivalent of Newton's Second Law ( ??-la ) for rotations about the center of mass of the spool. Assume all the forces below are magnitudes and clockwise (into the page) is considered the positive direction. -FIFrIa 4) Which of the following expressions relates the magnitudes of the translational about the center of mass a (recall the spool rolls without slipping on the surface acceleration of the spool's center of mass a and the spool's rotational acceleration 5) Now the string is attached as shown in the diagram below, still at a radius r * R. The spool is now pulled so it slides along the ground (which still has friction) but does not roll at all. What is the relationship between the magnitude of the force of tension and the force of frictio? Ff- FT

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