circular motion question

[max payne]

A car of mass 1200 kg is travelling anticlockwise around a horizontal circular track of
radius 240 m with a constant speed of 18 m s–1 (Figure 1.24).
c What is the magnitude of the car’s change in momentum when it moves from
A to B?
(Dont have the diagram but A is directly south of the centre and B is directly east of the centre.)
I thought the change in magnitude would be 0 since velocity and mass are constant? Sorry if this is an obvious question but thats what happens when you neglect your 1&2 units...thanks for your help.

[nbhindi]

The velocity isn't constant due to the changing direction of the car.....remember velocity is a vector quantity......hence both magnitude (speed) and direction have to be constant for constant velocity

[max payne]

HINT: The velocity isn't constant due to the changing direction of the car.....remember velocity is a vector quantity......hence both magnitude (speed) and direction have to be constant for constant velocity

Yeah I know but its asking for magnitude, so the direction is not needed...the answer is 30500kgm/s

[nbhindi]

A car of mass 1200 kg is travelling anticlockwise around a horizontal circular track of
radius 240 m with a constant speed of 18 m s–1 (Figure 1.24).
c What is the magnitude of the car’s change in momentum when it moves from
A to B?
(Dont have the diagram but A is directly south of the centre and B is directly east of the centre.)
I thought the change in magnitude would be 0 since velocity and mass are constant? Sorry if this is an obvious question but thats what happens when you neglect your 1&2 units...thanks for your help.

In my previous post was contesting the above statement.....as for the answer you have posted, i'm stumped

[Aurelian]

HINT: The velocity isn't constant due to the changing direction of the car.....remember velocity is a vector quantity......hence both magnitude (speed) and direction have to be constant for constant velocity

Yeah I know but its asking for magnitude, so the direction is not needed...the answer is 30500kgm/s

You need to consider the directions at first though.

Solution;

The car moves from B to A.

At B, the car is moving south. At A, the car is moving east. The magnitude of both momenta is the same (1200kg x 18ms-1 = 21600kgms-1), but the directions are different.

Looks like we need a triangle. We want the *change* in momentum from B to A - that is, the difference; "B - A" as it were. You should know how to do addition of basic vectors; to subtract the second from the first, merely reverse the direction of the second (that is, the direction at B).

We have a right triangle, with both sides being 21,600kgms-1. The magnitude of the momentum change will be the hypotenuse. Let's find that using pythagoras.

h^2 = 21,600^2 + 21,600^2 = 933,120,000
h = change in momentum = sqrt(933120000) = 30,547kgms-1 = 30,500kgms-1

Sorry if this is a bit unclear - it's hard explaining solutions like this (i.e., involving geometry) over the internet haha

EDIT: Whoops, did B-->A instead of A-->B. Same solution though.

[max payne]

HINT: The velocity isn't constant due to the changing direction of the car.....remember velocity is a vector quantity......hence both magnitude (speed) and direction have to be constant for constant velocity

Yeah I know but its asking for magnitude, so the direction is not needed...the answer is 30500kgm/s

You need to consider the directions at first though.

Solution;

The car moves from B to A.

At B, the car is moving south. At A, the car is moving east. The magnitude of both momenta is the same (1200kg x 18ms-1 = 21600kgms-1), but the directions are different.

Looks like we need a triangle. We want the *change* in momentum from B to A - that is, the difference; "B - A" as it were. You should know how to do addition of basic vectors; to subtract the second from the first, merely reverse the direction of the second (that is, the direction at B).

We have a right triangle, with both sides being 21,600kgms-1. The magnitude of the momentum change will be the hypotenuse. Let's find that using pythagoras.

h^2 = 21,600^2 + 21,600^2 = 933,120,000
h = change in momentum = sqrt(933120000) = 30,547kgms-1 = 30,500kgms-1

Sorry if this is a bit unclear - it's hard explaining solutions like this (i.e., involving geometry) over the internet haha

EDIT: Whoops, did B-->A instead of A-->B. Same solution though.

oh wow looks like it was an obvious question. thanks for that

[Aurelian]

oh wow looks like it was an obvious question. thanks for that

I wouldn't say 'obvious' by any means, I'd say unclear - your confusion was very understandable given the terms of the question!