Q14-9702_w17_qp_11
2017 paper (oct/nov) component 11
(This question is originally from Cambridge International Examination past paper)
14) The diagram shows a motorised vehicle for carrying one person.
The vehicle has two wheels on one axle. The passenger stands on a platform between the wheels.
The weight of the machine is 600 N. Its centre of mass is 200 mm in front of the axle. The wheel radius is 400 mm.
When stationary, a passenger of weight 600 N stands with his centre of mass 200 mm behind the axle to balance the machine. The motor is now switched on to provide a horizontal force of 90 N at the ground to move the vehicle forwards.
How far and in which direction must the passenger move his centre of mass to maintain balance?
- A 60 mm backwards
- B 60 mm forwards
- C 140 mm backwards
- D 140 mm forwards
Crux of the question: identify that the horizontal force 90 N (frictional force of ground acting at the wheel that actually made the vehicle moving) is acting at the ground instead of the centre of mass.
Applying principle of moment: Clockwise moment = anticlockwise moment
600(200)=600(x) +90(400) Where x is the distance from the c.o.m. of person to the axle.
\begin{equation}x=84000/60 \end{equation} \begin{equation} =140 \mathbf{mm} \end{equation}
Hence, the person needs to move forward by 60 mm in order to balance the system. Answer: B
*Just in case you are curious why the gravitational force is acting on the centre of mass of vehicle, while the 90 N horizontal force is not, keep in mind that the gravitational force acting at the centre of mass of a RIGID object is an “averaging” of all gravitational forces that are acting on the masses that constitute the object as a whole. However, since there is only one 90 N force acting at the ground (frictional force). The “average” of the 90 N force is exactly the 90 N force acting at the ground. So these two forces are acting at different locations even when they are acting at the same vehicle.