A wooden block of mass slides across a horizontal surface with coefficient of kinetic…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
A wooden block of mass m slides across a horizontal surface with coefficient of kinetic friction μk. While moving, the block suddenly separates into two pieces, masses m1 and m2, due to an internal chemical reaction. The reaction is instantaneous, and no material is ejected vertically; each piece continues to slide along the surface.
Immediately before separation the block’s speed is v0. Assume the coefficient of kinetic friction between each piece and the surface remains μk after separation.
(a) Determine the net horizontal external force acting on the two-piece system after separation. Explain your reasoning.
(b) Derive an expression for the horizontal acceleration of the system’s center of mass after separation.
(c) Show that the instantaneous separation does not change the speed of the center of mass at the moment just after the reaction.
(d) Determine, in terms of v0, μk, and g, the additional horizontal distance the center of mass travels after separation before coming to rest.