## Related questions with answers

A car is towing a boat on a trailer. The driver starts from rest and accelerates to a velocity of + 11 m/s in a time of 28 s. The combined mass of the boat and trailer is 410 kg. The frictional force acting on the trailer can be ignored. What is the tension in the hitch that connects the trailer to the car?

Solutions

VerifiedThe initial and final velocities of the vehicle are:

$v_0=0\,\text{m/s}\\ v=11\,\text{m/s}$

in the time:

$t=28\,\text{s}$

If the mass of the trailer is:

$m=410\,\text{kg}$

we have to calculate the tension of the hitch that connects the car and the trailer.

It is known that the car starts from rest $(v_0=0\ \frac{m}{s})$ and that its speed after $t=28\ \text{s}$ is $v=11\ \frac{m}{s}$. It is necessary to determine the tensile force $(T)$, if we ignore the friction $(f)$. The first step is to find the acceleration $(a)$ of the system (car + trailer), then by applying Newton's law we can determine the tensile force.

$\begin{align*} v&=11\ \frac{m}{s}\\ t&=28\ \text{s}\\ m&=410\ \text{kg} \end{align*}$

Determine the acceleration:

$\begin{align*} v&=v_0+a \cdot t\\ &=0+a \cdot t\\ &=a \cdot t\\ a&=\frac{v}{t}\\ \end{align*}$

According to Newton's law:

$\begin{align*} T&= m \cdot a\\ &=m \cdot \frac{v}{t}\\ &=410\ \text{kg} \cdot \frac{11\ \frac{m}{s}}{28\ \text{s}}\\ &=410\ \text{kg} \cdot 0.39\ \frac{m}{s^2}\\ &=161.1\ \text{N} \end{align*}$

Therefore, the final result is:

$\boxed{T=161.1\ \text{N}}$

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