Question

Some×, in physics, we appear to be equating two different quantities. Unit analysis is a useful sanity check when learning a new concept. Show that the base SI units for work and kinetic energy are the same:

a. kg·m/s^2
b. kg·m^2/s^2
c. kg·m^2/s
d. kg

Answer 1

Work and kinetic energy have the same SI units, which is kg·m²/s². The unit of work is obtained by multiplying force (kg·m/s²) by distance (m), and the kinetic energy uses the formula 1/2·mv², involving mass and velocity squared, leading to the same unit for both.

Step-by-step explanation:

The student asked to show that the base SI units for work and kinetic energy are the same. Work is defined as force applied over a distance, which in SI units is newton-meters or joules. Force itself is mass times acceleration, represented as kg·m/s². When you multiply force by distance (m), you get units of kg·m²/s², which is the unit for both work and kinetic energy. Kinetic energy is given by the formula K.E. = 1/2·mv², which involves mass (kg) and the square of velocity (m²/s²). Therefore, the SI units for both are the same.