# A level Maths help mechanics

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A tractor and its driver have a combined mass of 4m kilograms.

The tractor is towing a trailer of mass m kilograms in a straight line along a horizontal

road.

The tractor and trailer are connected by a horizontal tow bar, modelled as a light rigid

rod.

A driving force of 11 080 N and a total resistance force of 160 N act on the tractor.

A total resistance force of 600 N acts on the trailer.

The tractor and the trailer have an acceleration of 0.8 m s2

Work out m and the tension in the tow bar

At the instant the speed of the tractor reaches 18 km h1 the tow bar breaks.

The total resistance force acting on the trailer remains constant.

Starting from the instant the tow bar breaks, calculate the time taken until the speed

of the trailer reduces to 9 km h1

How would I go about working this out?

The tractor is towing a trailer of mass m kilograms in a straight line along a horizontal

road.

The tractor and trailer are connected by a horizontal tow bar, modelled as a light rigid

rod.

A driving force of 11 080 N and a total resistance force of 160 N act on the tractor.

A total resistance force of 600 N acts on the trailer.

The tractor and the trailer have an acceleration of 0.8 m s2

Work out m and the tension in the tow bar

At the instant the speed of the tractor reaches 18 km h1 the tow bar breaks.

The total resistance force acting on the trailer remains constant.

Starting from the instant the tow bar breaks, calculate the time taken until the speed

of the trailer reduces to 9 km h1

How would I go about working this out?

Last edited by ayman98763; 1 week ago

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#4

(Original post by

Plsss i need help

**ayman98763**)Plsss i need help

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#5

First, try using F=ma to create equations of motion for the trailer and the tractor.

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(Original post by

Are you just asking us to do your homework for you or do you need help with something

**Nagromicous**)Are you just asking us to do your homework for you or do you need help with something

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#7

(Original post by

I need help working out the tension and time taken? I've worked out the mass

**ayman98763**)I need help working out the tension and time taken? I've worked out the mass

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(Original post by

What have you got so far?

**squidge_gt**)What have you got so far?

and then i got the mass as 12900Newtons

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(Original post by

What is the resultant force, mass and acceleration of the trailer?

**Zelerate**)What is the resultant force, mass and acceleration of the trailer?

acceleration is 0.8ms^-2

and i think resultant force is 11080-600-160=10320 newtons

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#10

If you have the mass of the tractor + trailer (5m) to be 12900, then you can figure out m. Then consider the tractor forces: 11080-160-T=4m * 0.8

Last edited by Zelerate; 1 week ago

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(Original post by

If you have the mass of the tractor + trailer (5m) to be 12900, then you can figure out m. Then consider the tractor forces: 11080-160-T=m * 0.8

**Zelerate**)If you have the mass of the tractor + trailer (5m) to be 12900, then you can figure out m. Then consider the tractor forces: 11080-160-T=m * 0.8

10480-T =10320

so tension is 160 Newtons

is that right?

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#12

(Original post by

so 11080-600-T = 2580*4

10480-T =10320

so tension is 160 Newtons

is that right?

**ayman98763**)so 11080-600-T = 2580*4

10480-T =10320

so tension is 160 Newtons

is that right?

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(Original post by

Multiply 2580*4 by 0.8.

**Zelerate**)Multiply 2580*4 by 0.8.

10480-8256=2224 newtons

so 2224 newtons as tension.

Any idea about working out time taken, would that involve suvat equations?

Last edited by ayman98763; 1 week ago

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#14

(Original post by

2580*4=10320*0.8=8256

so 8256 newtons as tension.

Any idea about working out time taken, would that involve suvat equations?

**ayman98763**)2580*4=10320*0.8=8256

so 8256 newtons as tension.

Any idea about working out time taken, would that involve suvat equations?

For the time taken, it would indeed involve suvat equations as the acceleration is constant. v = u + at would be useful here. Since you know the force and the mass, you can work out the acceleration.

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(Original post by

11080 - 160 - 2580*4*0.8 = T = 2664.

For the time taken, it would indeed involve suvat equations as the acceleration is constant. v = u + at would be useful here. Since you know the force and the mass, you can work out the acceleration.

**Zelerate**)11080 - 160 - 2580*4*0.8 = T = 2664.

For the time taken, it would indeed involve suvat equations as the acceleration is constant. v = u + at would be useful here. Since you know the force and the mass, you can work out the acceleration.

s

u = 5ms-1 f=ma 10320/12900=0.8 i just get the same acceleration

v = 3.333ms-1

a =0.8

t ?

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#16

(Original post by

so i converted kmh^-1 to ms^-1

s

u = 5ms-1 f=ma 10320/12900=0.8 i just get the same acceleration

v = 3.333ms-1

a =0.8

t ?

**ayman98763**)so i converted kmh^-1 to ms^-1

s

u = 5ms-1 f=ma 10320/12900=0.8 i just get the same acceleration

v = 3.333ms-1

a =0.8

t ?

Also, as the speed is going from 18 km/h to 9 km/h, shouldn't your value of v should be 2.5?

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-600/12900/5= -600/2580 =-10/43

v=u + a t

2.5= 5 +(-10/43)t

-2.5/-10/43 =1075ms-1

v=u + a t

2.5= 5 +(-10/43)t

-2.5/-10/43 =1075ms-1

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(Original post by

Using F = ma (and a = F/m), the acceleration of the trailer should be -600/2560 as the tension no longer acts on it, and the mass is one fifth of 12900 (5m / 5)

Also, as the speed is going from 18 km/h to 9 km/h, shouldn't your value of v should be 2.5?

**Zelerate**)Using F = ma (and a = F/m), the acceleration of the trailer should be -600/2560 as the tension no longer acts on it, and the mass is one fifth of 12900 (5m / 5)

Also, as the speed is going from 18 km/h to 9 km/h, shouldn't your value of v should be 2.5?

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