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using dimensional analysis to make an educated guess in a physics question

Dimensional analysis describes the process of using standard international (SI) units to deduce an answer or equation. All units that describe a physical quantity can be derived from SI units

Example:

1. A 100 kg football player (player A) is running at ~5 m/s up a field when a 200 kg center (player B) steps in front of him. The football player in motion is abruptly stopped. What is the impulse imparted on player B by player A?

(a) 25 kg*m/s2

(b) 500 kg*m/s

(c) 2500 kg*m2/s2

(d) 10,000 Joules

answer
Suppose you’re having trouble remembering how to calculate impulse on test day. You recall that it has something to do with momentum and force, but do not remember the exact equation. Using dimensional analysis you can make an educated guess.

Step 1: gather your information: What information are we given in the problem?

velocity of A = 5 m/s
velocity of B = 0 m/s
mass of A = 100 kg
mass of B = 200 kg
impulse = ?

Step 2: use dimensional analysis to eliminate any answers with incorrect dimensions
What we need to do is to look at the units in each possible answer and work backwards to arrive at an equation that resembles what we recall about impulse. Answer (a) is in kg*m/s2 which recognize correctly as the units of the Newton or Force, which may be the right answer. Answer b is in mass*velocity units which is momentum, which also might be correct since we recall that impulse has something to do with momentum. We can eliminate (c) & (d) because they are in units of energy & power, respectively. On test day we’d have a 50-50 chance of getting this one right (between a & b).

Hopefully you’ll be better prepared & recall that impulse, I =pf – pi , or in plain words final momentum – initial momentum. In this case 100 * 5 – 0*5 = 500 kg*m/s.