Question

current attempt in progress
in which one of the following circumstances could mechanical energy not possibly be conserved, even if friction and air resistance are absent?
a car moves along level ground at a constant velocity
a car moves down a hill, its velocity continually increasing along the way
a car moves up a hill at a constant velocity
a car moves up a hill, its velocity continually decreasing along the way
using multiple attempts will impact your score.
20% score reduction after attempt 3

Explanation:

Step1: Recall the formula for mechanical energy

Mechanical energy \(E = K + U\), where \(K=\frac{1}{2}mv^{2}\) (kinetic energy) and \(U = mgh\) (gravitational potential energy).

Step2: Analyze each option

• Option 1: A car moves along level ground at a constant velocity. \(h\) (height) is constant (\(\Delta U=0\)) and \(v\) (speed) is constant (\(\Delta K = 0\)), so \(E\) is conserved.
• Option 2: A car moves down a hill, its velocity continually increasing. \(\Delta U<0\) (height decreases) and \(\Delta K>0\) (speed increases). If non - conservative forces (\(W_{nc}=0\) as \(friction = air\ resistance=0\)), by \(E_{f}-E_{i}=W_{nc}\), \(E\) can be conserved.
• Option 3: A car moves up a hill at a constant velocity. \(v\) (speed) is constant (\(\Delta K = 0\)) but \(h\) (height) increases (\(\Delta U>0\)). So \(E\) increases. Since \(W_{nc} = 0\) (no friction or air resistance), mechanical energy cannot be conserved.
• Option 4: A car moves up a hill, its velocity continually decreasing. \(\Delta U>0\) (height increases) and \(\Delta K<0\) (speed decreases). If non - conservative forces (\(W_{nc}=0\)), by \(E_{f}-E_{i}=W_{nc}\), \(E\) can be conserved.

Answer:

A car moves up a hill at a constant velocity.