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M1 question

Car of mass 800kg tows trailer of mass 300kg. Total resistance acting on them is 550N. Both particles, tow-bar is inextensible etc. Resistance acting on car is 800k and on trailer, is 300k.

I calculated the forward driving force to be 2750N and k = 0.5

d) The road is inclined at angle x where x = arcsin0.02. The resistance and driving force are unchanged.
calculate the acceleration of car and trailer.

thanks
Reply 1
never mind. I;ve solved it now.
Reply 2
How did you do it? Did you combine the mass?
Reply 3
You
How did you do it? Did you combine the mass?


no, resolve them individually. But this time, there is a component of the weight acting down the plane also (for the car and trailer).
Reply 4
Any chance you can show me how you did it? :redface:
Reply 5
You
Any chance you can show me how you did it? :redface:


okay:-

resolving for the Car, parallel to plane: -

2750 - 400 - T - 800gsin(arcsin 0.02) = 800a
T = 2193.2 - 800a (1)

resolving for the trailer, parallel to plane: -

T - 150 - 300gsin(arcsin 0.02) = 300a
T = 208.8 + 300a (2)

combining (1) and (2): -

2193.2 - 800a = 300a + 208.8
1100a = 1984.4
a = 1.80 ms^-2

hope this helps :smile:
Reply 6
hi,

just a bit6 confused about your notation on the original question. im not sure whether youve missed something out but it wounds wierd.

eg: "Total resistance acting on them is 550N" but then you say "Resistance acting on car is 800k and on trailer, is 300k." how can that be if the total is 550N?? also you say 800k is k a unit of something cos ive never heard of that! or is it 800k as in 800,000 ?

EDIT: ignore the above (just left in there so you can see my train of thought). you used k instead of K which got me confused!. so now im guessing K is a constant that you have to find? now i understand how you get K ( 550 = 800K + 300K ). but how did you find the driving force?

from your layout of the question it looks as though its two seperate parts. but in the first part you dont say whether the car is accelerating or still or what, so i dont know how you found the driving force. and the incline of the slope isnt mentioned until d) so i didnt think that applied for the first part.

could you just clear up a few things, or im gonna get paranoid because i think im missing something obvious!
Reply 7
kevinb456
hi,

just a bit6 confused about your notation on the original question. im not sure whether youve missed something out but it wounds wierd.

eg: "Total resistance acting on them is 550N" but then you say "Resistance acting on car is 800k and on trailer, is 300k." how can that be if the total is 550N?? also you say 800k is k a unit of something cos ive never heard of that! or is it 800k as in 800,000 ?

EDIT: ignore the above (just left in there so you can see my train of thought). you used k instead of K which got me confused!. so now im guessing K is a constant that you have to find? now i understand how you get K ( 550 = 800K + 300K ). but how did you find the driving force?

from your layout of the question it looks as though its two seperate parts. but in the first part you dont say whether the car is accelerating or still or what, so i dont know how you found the driving force. and the incline of the slope isnt mentioned until d) so i didnt think that applied for the first part.

could you just clear up a few things, or im gonna get paranoid because i think im missing something obvious!


Sorry, I answered part A, B and C.

This is the full question: -

A car of mass 800kg tows a trailer of mass 3300kg along a straight road. The car and trailer are acceleration at a uniform rate of 2ms^-2 and the total resistance acting on them is 550N. In an initial model the car and trailer are modelled as particles, the tow-bar connecting them as a light inextensible horizontal rod, and the road is assumed to be horizontal.
a) Calculate the driving force produced by the car's engine.

The resistance acting on the car is 800k N and 300k N on the trailer.
b) calculate k
c) calculate tension in the tow-bar

In refined model, the road is inclined at x=arcsin 0.02. The resistance and driving force are unchanged.
d) calculate the new acceleration of the car and trailer.

solution to a)

For car, using F = ma
let P = driving force
so P - T = ma
P - T = 800(2)
P = 1600 + T (1)

For trailer, using F = ma
T - 550 = 300(2)
T = 1150 N (2)

subs (2) into (1)
so P = 1600 + 1150
P = 2750 N

So the driving force is 2750N.