M1 stuck on braking car with trailer question

I can do a) and b) but don't see how there is enough information to do c).

Question is:
A car of mass 800Kg is towing a caravan of mass 300Kg along a horizontal road. the resistance forces (assumed constant) on the car and the caravan are 700N and 1200N respectively.
a) the car exerts a driving force of 3000N. Find the acceleration of the system and the tension in the coupling.

Let D = driving force, R1 = trailer resistance and R2 = car resistance.

D - R1 - R2 = ma

3000 - 1200 - 700 = 1100a

a = 1

ms^{-2}

T - R1 = ma

T - 1200 = 300(1)
T = 1500N

b) Find the force in the coupling when the system is travelling at a constant speed of 50 km/h.

At constant velocity a = 0

T - 1200 = ma = 0
T = 1200N

c) Find the force in the coupling when the car exerts a braking force of 2000N.

This is where I get stuck.

Resultant (car) = B + R2 - T

Resultant (trailer) = R1 + T

But because I don't know the acceleration (deceleration) how can I work this out?

Reply 1

ghostwalker

Repeat part (i), except where you had a driving force previously, you now have a braking force, and that will give you the deceleration.

Reply 2

acomber

Original post by ghostwalker

Repeat part (i), except where you had a driving force previously, you now have a braking force, and that will give you the deceleration.

You mean like this:

T - B - R2 = ma

T - 2000 - 700 = 800a

T - 2700 = 800a

T - 800a = 2700
and

R1 - T = ma

1200 - T = 300a

T + 300a = 1200

And build into two simultaneous equations?

I did try that but I don't get same answer as in book of 136.36N.

Reply 3

ghostwalker

Original post by acomber

...

No, I mean

-B-R1-R2= ma for the combined mass to get the acceleration to start.

Reply 4

Kavzaz

I think ghostwalker is correct.

Two simultaneous equations where the driving force is now replaced by a (negative) braking force.

So:

-T-700-2000 = 800a
T-1200=300a

I think this is right? I haven't solved it completely but will have a go now.

Reply 5

acomber

Original post by Kavzaz

You don't need simultaneous equations.

You get a from

-b - r1 -R2 = ma (only a is the unknown).

Then you find T by:

T - R1 = ma (here only T is unknown).

Reply 6

Millionmax

<--1200-- Caravan(300kg) --Tension-->

Taking forward as positive
Breaking force(b) + restive force 1(r1) +resistive force 2(r2) = resultant force of the system
b+r1+r2 = F = ma
-2000-700-1200 = -3900 = 1100a
a=-3900/1100 = -3.54545454545454
we now take just the caravan saying Tension(T) is an external force
T-1200 = ma =300x-3.54545454545454
T = 300x-3.54545454545454 +1200 = 136.36
= 136.4

Reply 7

MrToodles4

Original post by Millionmax

Does it have to be the caravans tension??? Can we use the car? Im very confused because i tried but i don't quite get the answer

Reply 8

ghostwalker

Original post by MrToodles4

Does it have to be the caravans tension??? Can we use the car? Im very confused because i tried but i don't quite get the answer

For the final bit of part c), you can focus on either the car or the caravan.

The caravan is marginally easier as the only forces acting are resistance and the coupling; for the car you have resistance, the coupling, and the braking force.

Post working if it's still not coming out.

Reply 9

MrToodles4

Original post by ghostwalker

Thank you so much, I really appreciate it. For part c I got the correct answer but I'm just wondering why do we ignore the driving force of 3000 N on the car?

And the only other bit bothering me about this question is part b. (when speed is constant 50kmh-1, so acceleration is 0). I know if we use the caravan we get T-1200 = 300*0. T is therefore 1200 N
However how would i find T when just using the car? I thought it would be T + 700 N = 800 * 0 (since acceleration is 0 and mass of car is 800kg). Would I need to take in mind the driving force of 3000 N here? But even then I can't seem to get the same tension as with the caravan. Any help is much appreciated

Reply 10

ghostwalker

Original post by MrToodles4

Thank you so much, I really appreciate it. For part c I got the correct answer but I'm just wondering why do we ignore the driving force of 3000 N on the car?

You either have a driving force or a braking force, but not both at the same time.
And the 3000N is in part a), not c)

And the only other bit bothering me about this question is part b. (when speed is constant 50kmh-1, so acceleration is 0). I know if we use the caravan we get T-1200 = 300*0. T is therefore 1200 N
However how would i find T when just using the car? I thought it would be T + 700 N = 800 * 0 (since acceleration is 0 and mass of car is 800kg). Would I need to take in mind the driving force of 3000 N here? But even then I can't seem to get the same tension as with the caravan. Any help is much appreciated

For part b) if you were to use the car, you'd need to know what the driving force is. But you're not told that. The 3000N is in part a) of the question - you now have a different set up.

Reply 11

MrToodles4

Original post by ghostwalker

You either have a driving force or a braking force, but not both at the same time.
And the 3000N is in part a), not c)

For part b) if you were to use the car, you'd need to know what the driving force is. But you're not told that. The 3000N is in part a) of the question - you now have a different set up.