- #1
Totally
- 26
- 2
1. The problem statement, all variables and given/known
A train of mass M is moving at uniform velocity v, being pulled by a locomotive with power P. A single cart of mass m gets detached. How far will it go before coming to stop? M, v, P and m are known.
The attempt at a solution
I know I'll need to find coeff. of kinetic friction in order to find the sliding distance. The force on the train before the cart gets detached is
\begin{equation*}
F-F_f=0
\end{equation*}
\begin{equation*}
\dfrac{P}{v}-\mu Mg=0
\end{equation*}
\begin{equation*}
\mu=\dfrac{P}{vMg}
\end{equation*}
Now, after the cart is detached I'm trying to use conservation of energy to find the distance
\begin{equation*}
\dfrac{1}{2}mv^2-\mu mgd=0
\end{equation*}
\begin{equation*}
d=\dfrac{v^2}{2\mu g}
\end{equation*}
Plugging in the $ \mu $ expression I get
\begin{equation*}
d=\dfrac{Mv^3}{2\mu P}
\end{equation*}
Using the M, v, P given initially and the kinetic friction that I found from the first part, I get the distance roughly 2.2 times too short when compared to the answer key. I'm sure I did the SI conversions correctly. Any ideas?
A train of mass M is moving at uniform velocity v, being pulled by a locomotive with power P. A single cart of mass m gets detached. How far will it go before coming to stop? M, v, P and m are known.
The attempt at a solution
I know I'll need to find coeff. of kinetic friction in order to find the sliding distance. The force on the train before the cart gets detached is
\begin{equation*}
F-F_f=0
\end{equation*}
\begin{equation*}
\dfrac{P}{v}-\mu Mg=0
\end{equation*}
\begin{equation*}
\mu=\dfrac{P}{vMg}
\end{equation*}
Now, after the cart is detached I'm trying to use conservation of energy to find the distance
\begin{equation*}
\dfrac{1}{2}mv^2-\mu mgd=0
\end{equation*}
\begin{equation*}
d=\dfrac{v^2}{2\mu g}
\end{equation*}
Plugging in the $ \mu $ expression I get
\begin{equation*}
d=\dfrac{Mv^3}{2\mu P}
\end{equation*}
Using the M, v, P given initially and the kinetic friction that I found from the first part, I get the distance roughly 2.2 times too short when compared to the answer key. I'm sure I did the SI conversions correctly. Any ideas?