8 A cylindrical tub of mass 250 kg is on a horizontal floor. Resistance to its motion other than that due to friction is negligible.
The first attempt to move the tub is by pulling it with a force of 150 N in the \(\mathbf { i }\) direction, as shown in Fig. 8.1.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6cca1e5e-82b0-487d-8048-b9db7745dea6-5_319_1358_511_392}
\captionsetup{labelformat=empty}
\caption{Fig. 8.1}
\end{figure}
- Calculate the acceleration of the tub if friction is ignored.
In fact, there is friction and the tub does not move.
- Write down the magnitude and direction of the frictional force opposing the pull.
Two more forces are now added to the 150 N force in a second attempt to move the tub, as shown in Fig. 8.2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6cca1e5e-82b0-487d-8048-b9db7745dea6-5_502_935_1411_607}
\captionsetup{labelformat=empty}
\caption{Fig. 8.2}
\end{figure}
Angle \(\theta\) is acute and chosen so that the resultant of the three forces is in the \(\mathbf { i }\) direction. - Determine the value of \(\theta\) and the resultant of the three forces.
With this resultant force, the tub moves with constant acceleration and travels 1 metre from rest in 2 seconds.
- Show that the magnitude of the friction acting on the tub is 661 N , correct to 3 significant figures.
When the speed of the tub is \(1.8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), it comes to a part of the floor where the friction on the tub is 200 N greater. The pulling forces stay the same.
- Find the velocity of the tub when it has moved a further 1.65 m .
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