Question

question 12 (6 points)
(03.02 hc)
think of a book at rest on a flat leveled surface and another book (same type) that is sliding and slowing down to a complete stop on
the same surface.
a. what force(s) is on the sliding book that is not on the book at rest? explain why.
b. if the sliding book was speeding up instead, describe how the free body diagram would be drawn differently than the book
at rest.

Explanation:

For part a, when analyzing forces on an object, we consider Newton's laws. A book at rest has balanced forces (gravity \(F_g = mg\) downward and normal force \(F_N\) upward, \(F_g=F_N\)). A sliding book (assuming no external applied force besides initial push) has the same \(F_g\) and \(F_N\) (since mass \(m\) and \(g = 9.8\ m/s^{2}\) are constant and surface is same, so normal force which counteracts gravity in vertical direction is same), but also has a frictional force \(F_f=\mu_k F_N\) (kinetic friction) opposing its motion.
For part b, if the book is speeding up, there is a net force in the direction of motion. In a free - body diagram, in addition to \(F_g\), \(F_N\), and \(F_f\) (if there is a surface - related friction), there would be an applied force \(F_{app}\) (e.g., someone pushing the book harder than the frictional force). The length of the force vector for the applied force (if present) and the resultant force (using vector addition \(F_{net}=\sqrt{(F_{app}-F_f)^2+(F_N - F_g)^2}\), but since \(F_N = F_g\), \(F_{net}=F_{app}-F_f\)) would be different from the case of a book slowing down (where \(F_{net}=F_f\) if no applied force, or \(F_{net}=F_f - F_{app}\) if there is a small applied force in the direction of motion but \(F_f>F_{app}\)).

Answer:

a. The book at rest has two forces: gravitational force (\(F_g = mg\), downward) and normal force (\(F_N\), upward, \(F_N = F_g\)). The sliding book has three forces: \(F_g\), \(F_N\) (same magnitudes as for the resting book since \(m\) and \(g\) and surface are same), and kinetic frictional force (\(F_f=\mu_k F_N\), opposite to the direction of motion).
b. If the sliding book is speeding up, there is an unbalanced force in the direction of motion. In the free - body diagram, if we assume a horizontal direction, there would be a force (e.g., an applied force \(F_{app}\)) in the direction of motion with \(F_{app}>F_f\) (kinetic friction). The length of the vector representing the net force (\(F_{net}=F_{app}-F_f\)) would be longer than in the case of a book slowing down (where \(F_{net}=F_f\) if no applied force or \(F_{net}=F_f - F_{app}\) if \(F_{app}