Question

A spool of thread, free to unwind, is on a horizontal surface (with friction) and pulled directly upward (+y) at all times. The spool rolls without slipping on the floor. The spool has a mass M, moment of inertia I, and a radius of R. Assume the string is wrapped around the spool at a radius r (where r < R). spool rolling on the floor

Which equation below is a correct expression of Newton’s Second Law ( ΣF=ma ) in the x (horizontal) -direction for this situation. Assume all the forces below are magnitudes and that to the right is considered the positive direction.

a. F_T - Ff= Max
b. F_T+Ff= Max
c. Ff= Max

Answer 1

The correct application of Newton’s Second Law for the spool being pulled by a string is described by the equation FT - Ff = Max, where FT is the tension in the string, Ff is the frictional force, M is the mass of the spool, and ax is its acceleration. Option a.

Step-by-step explanation:

The correct equation to describe Newton’s Second Law (ΣF=ma) in the x-direction for a spool rolling without slipping on a surface is a. FT - Ff= Max. This is because the spool is rolling without slipping, meaning that the static friction force (Ff) acts in the opposite direction of the tension force (FT) in the string.

The net force in the x-direction is then the difference between these two forces, which equals the mass of the spool (M) times its acceleration in the x-direction (ax).

It is important to note that r, the radius at which the string is wrapped around the spool, does influence torque, with an equation of t = mr²α, where α represents angular acceleration. However, this does not directly change the net force equation for translational motion. So Option a.

Answer 2

The Correct Answer is "D"

Step-by-step explanation:

For Detail of this answer Please see the attached file.