2 A box of mass 8 kg slides on a horizontal table against a constant resistance of 11.2 N .
- What horizontal force is applied to the box if it is sliding with acceleration of magnitude \(2 \mathrm {~ms} ^ { - 2 }\) ?
Fig. 7 shows the box of mass 8 kg on a long, rough, horizontal table. A sphere of mass 6 kg is attached to the box by means of a light inextensible string that passes over a smooth pulley. The section of the string between the pulley and the box is parallel to the table. The constant frictional force of 11.2 N opposes the motion of the box. A force of 105 N parallel to the table acts on the box in the direction shown, and the acceleration of the system is in that direction.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0fbef619-ad15-4e46-be35-e17fed9952c0-2_372_878_870_683}
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\caption{Fig. 7}
\end{figure} - What information in the question indicates that while the string is taut the box and sphere have the same acceleration?
- Draw two separate diagrams, one showing all the horizontal forces acting on the box and the other showing all the forces acting on the sphere.
- Show that the magnitude of the acceleration of the system is \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) and find the tension in the string.
The system is stationary when the sphere is at point P . When the sphere is 1.8 m above P the string breaks, leaving the sphere moving upwards at a speed of \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- (A) Write down the value of the acceleration of the sphere after the string breaks.
(B) The sphere passes through P again at time \(T\) seconds after the string breaks. Show that \(T\) is the positive root of the equation \(4.9 T ^ { 2 } - 3 T - 1.8 = 0\).
( \(C\) ) Using part ( \(B\) ), or otherwise, calculate the total time that elapses after the sphere moves from P before the sphere again passes through P .