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Chapter 9: Problem 22

A toboggan of mass \(8.6 \mathrm{kg}\) is moving horizontally at \(23 \mathrm{km} / \mathrm{h}\). As it passes under a tree, \(15 \mathrm{kg}\) of snow drop onto it. Find its subsequent speed.

Short Answer

Expert verified
The subsequent speed of the toboggan after the snow falls on it will be approximately \(v' = 3.37 \, m/s \).

Step by step solution

01

Identify the Known and Convert all units

First identify the given quantities: mass of toboggan \(m_1 = 8.6 \, kg\), its speed \(v_1 = 23 \, km/h = 6.39 \, m/s\) (converted from km/h to m/s), mass of snow \(m_2 = 15 \, kg\). The subsequent speed of the combined snow and toboggan, \(v'\), is what we need to find.
02

Apply the Principle of Conservation of Momentum

The total momentum before the snow falls shall equal the total momentum after. Hence, we can write the equation as: \(m_1*v_1 = (m_1 + m_2)*v'\)
03

Solve for the unknown

Rearrange the equation to solve for \(v'\) by dividing both sides by \((m_1 + m_2)\). This will give: \(v' = \frac{m_1*v_1}{m_1 + m_2}\)
04

Calculate the unknown

Substitute the known values into the equation to get: \(v' = \frac{8.6*6.39}{8.6 + 15} \, m/s\)Calculating the above will give the subsequent speed of the toboggan with the snow on it.
05

Evaluate the Result

Perform the calculation, and also make sure that the answer makes sense. In this case, it should be less than the initial speed of the toboggan as snow falling adds mass to the toboggan without adding any speed.

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