Finding the Dimensionally Consistent Powers for Acceleration Equation

  • Thread starter Thread starter swatmedic05
  • Start date Start date
AI Thread Summary
To determine the powers p and q for the equation A=V^p t^q that ensure dimensional consistency, the dimensions of acceleration (L^1 T^-2) must match the combined dimensions of velocity and time. The expression for velocity is L^1 T^-1, and time is represented as T. By substituting these into the equation, we find that (L^1 T^-1)^p (T)^q must equal L^1 T^-2. Solving the resulting equations for L and T gives p=1 and q=-2. This basic dimensionality problem illustrates the importance of matching dimensions in physics equations.
swatmedic05
Messages
42
Reaction score
0
Acceleration is related to velocity and time by the following expression: A=V^p t^q

Find the powers p and q that make this equation dimensionally consistent.
 
Physics news on Phys.org
You know that acceleration is L^1 T^-2, that velocity is L^1 T^-1 and t is of course T.

V^p t^q = (L^1 T^{-1})^p (T)^q = (L^1 T^{-2}) = A

this is your very basic dimensionality problem. Try to look over some examples and post your work if you need further help.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Thread 'Struggle to understand the concept of the question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »

Similar threads

Find the powers p and q that make this equation dimensionally consistent
Replies
6
Views
6K
Hamiltonian Function thru new Variables Q,P -- Show that Q is cyclic
Replies
5
Views
734
V/I: Power from Potential Difference & Current
Replies
5
Views
1K
Dimensional Consistency of Acceleration Equation: Step-by-Step Guide
Replies
29
Views
4K
Find the power needed to accelerate this elevator downward
Replies
4
Views
1K
Are suvat equations valid in 2 dimensional motion for constant acceleration?
Replies
5
Views
1K
When is power constant in this scenario?
Replies
25
Views
2K
Finding a Parametric Solution for Particle Trajectory in Magnetic Field
Replies
3
Views
2K
Two spring-coupled masses in an electric field (one of the masses is charged)
Replies
1
Views
915
Query related to Two-Dimensional Motion
Replies
9
Views
1K

Hot Threads

Recent Insights

Back
Top