What is the dimension of work? (2022)

What is the dimension of work? (2022)

Step 1: Understand that work is defined as force applied over a distance.
Step 2: Recall that force is calculated as mass times acceleration (F = m * a).
Step 3: Identify the dimensions of mass (M), distance (L), and acceleration (a).
Step 4: The dimension of mass is M^1 (one mass unit).
Step 5: The dimension of distance is L^1 (one length unit).
Step 6: Acceleration is the change in velocity over time, which has dimensions of L^1T^-2 (length per time squared).
Step 7: Substitute the dimension of acceleration into the force equation: F = M^1 * (L^1T^-2).
Step 8: Combine the dimensions: F = M^1L^1T^-2.
Step 9: Now, since work is force times distance, multiply the dimensions of force by the dimension of distance: Work = F * L.
Step 10: Substitute the dimensions: Work = (M^1L^1T^-2) * (L^1).
Step 11: Combine the dimensions: Work = M^1L^(1+1)T^-2 = M^1L^2T^-2.
Step 12: Conclude that the dimension of work is M^1L^2T^-2.

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