Fig. 1 is a force diagram for an automated library trolley as it travels across a smooth concrete floor. The trolley carries boxes of returned books. Its ba...
Question 1 Report
Fig. 1 is a force diagram for an automated library trolley as it travels across a smooth concrete floor. The trolley carries boxes of returned books. Its battery-powered motor provides a force of 180 N towards the north. A side roller against a guide rail produces a force of 240 N towards the east. The students assume that friction and air resistance are too small to affect the calculation. The two forces act at right angles.
(a) Calculate the size of the resultant force on the trolley. Give your answer in N. [3]
(b) Describe the direction of the resultant force, using north and east. [1]
(c) Use the resultant force to state what happens to the trolley's velocity while these forces act. [2]
(d) Draw a labelled arrow on Fig. 1 to show a third force that would make the resultant force zero. [2]
(e) Explain why the trolley can still move at a steady velocity when the resultant force is zero. [2]
Answer Details
(a) The forces are at right angles, so use Pythagoras' theorem:
\[R^2=180^2+240^2=32400+57600=90000\]
\[R=\sqrt{90000}=300\text{ N}\]
The resultant force is 300 N. [3]
(b) The resultant acts towards the north-east. [1]
(c) Since there is a non-zero resultant force, the trolley accelerates and its velocity changes in the north-east direction. [2]
(d) To make the resultant zero, a third force must be equal and opposite to the 300 N north-east resultant: 300 N towards the south-west.
[2]
(e) A zero resultant force means zero acceleration, so there is no change in velocity. An object already moving therefore continues at constant velocity. [2]
Download The App On Google Playstore
Everything you need to excel in your exams
