Spike claims that dimensional analysis shows that the correct expression for change in velocity, , is , where m is mass, t is time, and F is the magnitude of force. Carla says that can't be true because the dimensions of force are . Which one, if either, is correct?
A)Spike, because .
B)Spike, because .
C)Carla, because .
D)Carla, because .
E)Spike, because the dimensions of force are .

Question

Spike claims that dimensional analysis shows that the correct expression for change in velocity,  , is  , where m is mass, t is time, and F is the magnitude of force. Carla says that can't be true because the dimensions of force are  . Which one, if either, is correct?
A)Spike, because . 
B)Spike, because . 
C)Carla, because . 
D)Carla, because . 
E)Spike, because the dimensions of force are .

Quizplus · Accepted Answer

The correct expression for change in velocity must be dimensionally consistent, meaning that the dimensions of the left side must be equal to those of the right side. From the given expressions, we have:

dimension of Δv = [L]/[T]
dimension of m = [M]
dimension of t = [T]
dimension of F = [M][L]/[T]^2

Applying dimensional analysis to the proposed expression:

Δv = F/m * t

dimension of F/m = [M][L]/[T]^2 /[M] = [L]/[T]^2

dimension of t = [T]

dimension of Δv = [L]/[T]

Therefore, the dimensions of the right side are [L]/[T] * [T] = [L], which do not match the required dimensions of Δv. Carla is correct that the expression proposed by Spike cannot be true because the dimensions of force are not consistent with the dimensions of Δv.

Spike Claims That Dimensional Analysis Shows That the Correct Expression