Homework Statement
Why are the Center of Momentum velocities of masses after a 2D elastic collision anti-parallel? (as in the following diagram)
Homework Equations
CM_Velocity = (∑m_i*v_i)/(∑m_i)
The Attempt at a Solution
This is not actually a problem I have to do. I am just looking for a...
Yes it is meant to, my mistake for lack of clarity. From now on I will use ##dU## instead of ##du## to represent the derivative of ##U##
Does it ##=F+dU/dx##?
Ok, I can see why ##ΔU \neq dU## in this case. After all, ##ΔU## represents a real change in potential, not an infinitesimally small...
Homework Statement
Where U is potential energy, show that F = -du/dx
Homework Equations
ΔU = U(x) - U(x_0)
$$ΔU = U(x) - U(x_0) = \int_{x_0}^{x}Fdx \qquad (1)$$
The Attempt at a Solution
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I am confused why
$$\frac{d}{dx}ΔU = \frac{du}{dx} \qquad (2)$$...
Homework Statement
Come up with expressions for centripetal acceleration at the top of the small hump and the bottom of the loop. (this is one substep in a larger problem)
Homework Equations
f = ma
The Attempt at a Solution
Taking down to be negative, I believe that the f = ma equation at...
Homework Statement
Find the arclength of $$r(t) = <{t}^2/2,{t}^3/3>$$ from t=-1 to t=1
Homework Equations
I have used this equation for arclength $$\int_{-1}^{1}|{r}'(t)|dt$$
The Attempt at a Solution
After integrating (using u substitution) I have the solution...