A museum conservator moves a heavy display case using four small air pads. The pads reduce friction, but a slight frictional force of 25 N remains. Two work...
Question 1 Report
A museum conservator moves a heavy display case using four small air pads. The pads reduce friction, but a slight frictional force of 25 N remains. Two workers push to the east with forces of 40 N and 35 N. A third worker pushes west with 15 N to guide the case around a corner. The case is already moving east. The conservator needs to decide whether its velocity will increase, decrease, or stay the same. All forces given are horizontal.
(a) Calculate the total force to the east. [1]
(b) Calculate the total force to the west. [1]
(c) Calculate the resultant force on the display case. [2]
(d) Explain the effect of this resultant force on the eastward velocity. [2]
(e) Give one change that would make the resultant force zero. [2]
Answer Details
(a) Total eastward force:
\[40+35=75\text{ N}.\]
[1]
(b) Total westward force includes the worker's push and friction:
\[15+25=40\text{ N}.\]
[1]
(c)
\[F_\text{resultant}=75-40=35\text{ N}\]
The resultant force is \(35\text{ N}\) east. [2]
(d) The resultant force is eastwards, so the display case accelerates eastwards. Since it is already moving east, its eastward velocity increases. [2]
(e) One valid change is to increase the westward push from \(15\text{ N}\) to \(50\text{ N}\). This adds \(35\text{ N}\) westwards, making the westward total \(75\text{ N}\), equal to the eastward total. Reducing the eastward pushes by a total of \(35\text{ N}\) would also be valid. [2]
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