Question 7
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
Reference: Past Exam Paper – November 2017 Paper 11 Q14
Solution:
Answer:
B.
To maintain balance,
Anti-clockwise moment = Clockwise
moment
The weight of the machine
exerts a clockwise moment (= 600×200).
The weight of the person
exerts an anti-clockwise moment (= 600×200).
To move forward, the
machine exerts a force of 90N in the direction of motion. This provides an anti-clockwise
moment (= 90×400).
When in motion,
(600×200) + (90×400) = (600×200)
When the motor is on, the anti-clockwise
moment is greater than the clockwise moment.
To maintain balance,
Anti-clockwise moment =
Clockwise moment
So, to maintain balance, the
anti-clockwise moment should be reduced so that it equals the clockwise moment.
The moment exerted by the
weight of the person can be changed by moving his centre of mass. To reduce the
anti-clockwise moment, the person should bring his centre of mass towards the
pivot (axle). That is, he needs to move forwards. This reduced the
distance of his weight from the axle.
Let the distance moved forwards
to maintain balance be x.
[600 × (200 – x)] + (90×400) = (600×200)
200 – x = [(600×200) – (90×400)] / 600 = 140
x = 200 – 240 = 60 mm
thank you very much
ReplyDeletemay Allah bless you!!!!!!!!!!!! I spent like an hour trying to get anything but c thank you so very much!!
ReplyDeletesry but why move forward produce anticlockwise moment?
ReplyDeletethe centre of mass of the person is to the left of the axle (pivot). this causes an anticlockwise moment.
DeleteIf all car's wheel rotates clockwise then, it'll go backwards?
ReplyDeleteas the wheel rotates, at the point of contact with the road, it exerts a force backwards. from Newton's 3rd law, there would be a force in the opposite direction and of the same magnitude. this force is the force of friction between the road and the wheel
DeleteVery nice . I am confused how the motor is creating an anticlockwise moment even though it clearly shown the direction of motion is to the right, so shouldn't it be clockwise?
ReplyDeleteConsider the axle being the pivot.
DeleteThe motor exerts a force forwards, on the ground.
Relative to the axle (pivot), this provides an anticlockwise moment.
Much love, Thanks
DeleteI don't understand if it is moving rightwards that means the wheels moving in clockwise direction hence the 90N should contribute to clockwise moment pls explain asap
ReplyDeletejust forget that the wheel is moving clockwise or anticlockwise. actually, the correct word to use is 'rotating' instead of 'moving'. A rotating object on itself does not produce a moment.
Deletethe questions tell us that the force of 90N is forward along the surface. SO, it is just below the axles. Now, consider the axle as the pivot and the forward acting forward along the surface. (include it on the diagram). this force produces an anticlockwise moment.
how are you such a genius?
DeleteThank you for your reply! I understood it with the context of the question but does this mean a wheel rotating clockwise will ALWAYS produce anticlockwise moment ?
ReplyDeleteYou only need to consider the direction of the force relative to the position of the pivot (here, the axle).
DeleteFrom this, you can tell whether it is clockwise or anticlockwise.
SO, it's better to follow this thought process rather than trying to say that in a specific case, it is always clockwise or anticlockwise
THANK U SO MUCH!!
DeleteMy AS levels are starting on 18th of Feb. I am averaging about 34 to 35 in mcq and 53 to 54 in structured.how much do I need out of 140 including practical if I want an A star in A levels.
ReplyDeletethis depends on the 'grade threshold' document which is only available after the exams.
Deleteso, the best that you can think of right now is to score the maximum mark in all papers. Try to score the best result
Who ever is behind this blog is such a genius im truly impressed haha
ReplyDeletecould u pls tell how the 90N force provides a anticlockwise moment.
ReplyDeleteThe force of 90 N is horizontally to the right and below the axle (taken as the pivot). This causes an anticlockwise moment about the axle.
Deletewoulnt the 90N force create a torque?
ReplyDeleteyes, and this is why the passenger moves his centre of mass so that this creates an opposing torque and maintain balance
Delete