Day: February 10, 2023

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202302101153 Exercise 26.2

If required take g=9.8\,\mathrm{m\,s^{-2}}.

1. Two trucks, masses 30\,\mathrm{kg} and 20\,\mathrm{kg}, travelling at 6\,\mathrm{m\,s^{-1}} and 2\,\mathrm{m\,s^{-1}} respectively in the same direction, collide and continue together. Find the loss of KE due to the collision, and the percentage loss of energy.
2. Two masses, of 3\,\mathrm{kg} and 2\,\mathrm{kg}, move towards each other at speeds 2\,\mathrm{m\,s^{-1}} and 1\,\mathrm{m\,s^{-1}} respectively. After colliding they move together. Find the percentage loss of energy in the collision.
3. A force of 2\,\mathrm{N} is applied for 5\,\mathrm{s} to a mass of 2\,\mathrm{kg} resting on a smooth horizontal surface. The mass now collides with a second mass of 3\,\mathrm{kg} at rest, and they continue together. Find the common velocity and the loss of KE in the impact.

Extracted from A. Godman & J. F. Talbert. (1975). Additional Mathematics Pure and Applied in SI Units.

Roughwork.

1.

\begin{aligned} m_1u_1+m_2u_2 & = (m_1+m_2)v \\ (30)(6) + (20)(2) & = (30+20)v \\ v& = 4.4\,\mathrm{m\,s^{-1}}\\ \end{aligned}

\begin{aligned} \textrm{KE}_\textrm{initial} & = \frac{1}{2}(30)(6)^2 + \frac{1}{2}(20)(2)^2 = 580\,\mathrm{J} \\ \textrm{KE}_\textrm{final} & = \frac{1}{2}(30+20)(4.4)^2 = 484\,\mathrm{J}\\ \Delta\textrm{KE} & = -96\,\mathrm{J}\\ \end{aligned}

2. Not to be attempted.

3.

\begin{aligned} F_{\textrm{net}} & = \frac{\Delta p}{\Delta t} \\ 2 & = \frac{(2)(v-0)}{5} \\ v & = 5\,\mathrm{m\,s^{-1}} \\ \end{aligned}

\begin{aligned} m_1u_1+m_2u_2 & = (m_1+m_2)v \\ (2)(5)+(3)(0) & = (2+3)v \\ v & = 2\,\mathrm{m\,s^{-1}} \\ \end{aligned}

Not to be completed.