Chapter 14: Dimensional Analysis.

Question 1

What Letter do we use for the Dimension of Mass?

Answer 1

M.

Question 2

What Letter do we use for the Dimension of Length?

Answer 2

L.

Question 3

What Letter do we use for the Dimension of Time?

Answer 3

T.

Question 4

What are the dimensions for Speed (Velocity)?

Answer 4

L T^-1 (Distance (L)/ Time (T)).

Question 5

What are the dimensions for Acceleration?

Answer 5

L T^-2 (Change in Velocity (LT^-1)/ Time (T)).

Question 6

What are the dimensions for Force?

Answer 6

M L T^-2 (Mass (M) x Acceleration (LT^-2)):

Question 7

What are the dimensions for Coefficient of Friction (μ)?

Answer 7

1 (Dimensionless) (Fmax (MLT^-2) = μ x Reaction Force (MLT^-2)).

Question 8

How do you show something is dimensionally consistent?

Answer 8

Prove both sides of the equation are equal to each other.

Question 9

What are the dimensions of sinθ?

Answer 9

sinθ = O/H = L/L = 1.
Therefore it is dimensionless.

Question 10

What are the dimensions of cosθ?

Answer 10

cosθ = A/H = L/L = 1.
Therefore it is dimensionless.

Question 11

What are the dimensions of tanθ?

Answer 11

tanθ = O/A = L/L = 1.
Therefore it is dimensionless.

Question 12

What are the dimensions for Kinetic Energy (KE)?

Answer 12

M L^2 T^-2 –> (KE = 1/2mv^2 - Mass (M) x Velocity^2 (L T^-1)).

Question 13

What are the dimensions for Gravitational Potential Energy (GPE)?

Answer 13

M L^2 T^-2 –> (GPE = mgh - Mass (M) x Gravity (L T^-2) x Height (L)).

Question 14

What are the dimensions for Impulse?

Answer 14

M L T^-1 –> (I = Ft - Force (M L T^-2) x Time (T)).

Question 15

What are the dimensions for Pressure?

Answer 15

M L^-1 T^-2 –> (P = F/A - Force (M L T^-2) ÷ Area (L^2)).

Question 16

What are the dimensions for Density?

Answer 16

M L T^-1 –> (ρ = M/V - Mass (M) ÷ Volume (L^3)).

Question 17

What are the dimensions for Work Done?

Answer 17

M L^2 T^-2 –> (W.D = F x d - Force (M L T^-2) x Distance (L)).

Question 18

What are the dimensions for Momentum?

Answer 18

M L T^-1 –> (Momentum = M x v - Mass (M) x Velocity (L T^-1)).

Question 19

What are the dimensions for Volume?

Answer 19

Length³ = L³.

Question 20

What are the dimensions for Power?

Answer 20

M L^2 T^-3 –> (P = F x v - Force (M L T^-2) x Velocity (L T^-1)).