## Related questions with answers

The van is traveling at $20 \mathrm{~km} / \mathrm{h}$ when the coupling of the trailer at $A$ fails. If the trailer has a mass of $250 \mathrm{~kg}$ and coasts $45 \mathrm{~m}$ before coming to rest, determine the constant horizontal force $F$ created by rolling friction which causes the trailer to stop.

Solution

VerifiedGiven: $v_i = 20 \cdot \dfrac{1000}{3600} = 5.56$ m/s, $m = 250$ kg, $s = 45$ m.

The trailer at the beginning has the initial velocity $v_i$. Its final velocity is $v_f = 0$ m/s, because after it travels for $45$ meters, it will stop. So, we can calculate the magnitude of acceleration:

$\begin{align*} v_f^2 &= v_i^2 - 2as \\ 0 &= 5.56^2 - 2\cdot a \cdot 45 \\ 90a &= 30.86 \\ a &= 0.343 \, \text{m/s}^2. \end{align*}$

On the trailer acts only the force of friction, so the equation of motion is:

$\begin{align*} F_{\text{friction}} &= m a \\ &= 250 \cdot 0.343 \\ &= 85.73 \, \text{N.} \end{align*}$

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