Question

Are the units of the formula ma = mv²/2 dimensionally consistent? select the single best answer.

a.no-ma has units of kg⋅m/s² and 1/2mv² has units of kg⋅m²/s²
b.no-ma has units of kg⋅m/s and 1/2m² has units of kg⋅m²/s²
c.yes-both ma and 1/2mv² have units of kg⋅m²/s²
d.no -ma has units of kg⋅m²/s² and 1/2mv² has units of kg⋅m/s²
e.yes-both ma and 1/2mv² have units of kg⋅m/s
f.yes-the units of m cancel on both sides.
g.yes-both ma and 1/2mv² have units of kg⋅m/s

Answer 1

The formula ma = mv²/2 is not dimensionally consistent; ma represents force with units of kg⋅m/s² while mv²/2 represents kinetic energy with units of kg⋅m²/s².

Step-by-step explanation:

The units of the formula ma = mv²/2 are dimensionally consistent. The term ma has units of kg⋅m/s², which represent force (newtons, N), and the term mv²/2 represents kinetic energy, with units of kg⋅m²/s² (joules, J). Dimensional analysis of both sides of the equation confirm that they are not equivalent since force and energy have different units. Therefore, the correct answer is a. no - ma has units of kg⋅m/s² and 1/2mv² has units of kg⋅m²/s².