Question

as the block slides across the floor, what happens to its kinetic energy ( k ), potential energy ( u ), and total mechanical energy ( e )? (\bigcirc) ( k ) decreases; ( u ) increases; ( e ) decreases (\bigcirc) ( k ) increases; ( u ) decreases; ( e ) decreases (\bigcirc) ( k ) decreases; ( u ) stays the same; ( e ) decreases (\bigcirc) ( k ) increases; ( u ) stays the same; ( e ) decreases (\bigcirc) ( k ) decreases; ( u ) increases; ( e ) stays the same (\bigcirc) ( k ) increases; ( u ) decreases; ( e ) stays the same

Explanation:

1. Kinetic Energy (K): When a block slides across a floor, there is friction acting against its motion. Friction does negative work on the block, which means the block's speed decreases (assuming no other force is accelerating it). Since kinetic energy \( K = \frac{1}{2}mv^2 \), a decrease in speed (\( v \)) leads to a decrease in \( K \).
2. Potential Energy (U): The block is sliding horizontally across the floor, so its height relative to the ground (or the reference point for gravitational potential energy) does not change. Gravitational potential energy \( U = mgh \), and since \( h \) (height) is constant, \( U \) stays the same. There's no indication of elastic potential energy changes here (like a spring), so we consider gravitational potential energy, which remains constant.
3. Total Mechanical Energy (E): Total mechanical energy is \( E = K + U \). We know \( K \) decreases and \( U \) stays the same. Additionally, friction is a non - conservative force. Non - conservative forces dissipate mechanical energy (convert it into other forms like heat), so the total mechanical energy \( E \) of the block - Earth system (considering gravitational potential energy) will decrease because energy is lost to friction.

Looking at the options, the one that matches is "K decreases; U stays the same; E decreases".

Answer:

K decreases; U stays the same; E decreases (the option with this description among the given choices)