The Regular Work

Classical Mechanics Level 2

Rigby and Mordecai were given a job by Benson the Manager. They were supposed to carry a heavy electric motor placed on a light board of length 2.00 m. Rigby, being the smaller one, lifts at one end with a force of only 400. N., while Mordecai lifts at the other end with a force 600. N. Both of them exert these forces straight up. The board and heavy electric motor must both be balanced, or else Benson would deduct from their salary.

Where along the board should the motor be placed?

Details and Assumptions

  • Treat the motor as a point mass.

  • Neglect the mass of the board.

1.5 m. from Rigby 1.6 m. from Mordecai 1.2 m. from Rigby 1.0 m. from either of them

Captain Awesome by Captain Awesome , 23, Philippines

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8 solutions

Amj Gatsby
Apr 2, 2014

600*x = 400 * (2-x)

12 Helpful 0 Interesting 0 Brilliant 0 Confused

0.8

Saket Kumar - 7 years, 2 months ago

Sorry, but I think you have the brackets misplaced. It should be 600 (2-x)=400 x

Velayuthan Segar - 7 years, 2 months ago

I think It should be nearer to Powerfull man i.e 1.6 from Mordecai.. cause he is applying greater FOrce so to balance....it should be placed nearer to Mordecai..... ..if i m wrong...explain? plzzzzz

SulpHuric Acid - 7 years, 2 months ago

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your correct , is should be nearer to the Mordecai...... But as you say, if it 1.6 m from him it is actullay far away from him when compared to Rigby(2-1.6) is .4 m so its near to rigby.........

Saravanan Rajenderan - 7 years, 2 months ago

IT's about balancing of moment, with a force of 400N and 600N on either end. let motor be at a distance of x from 4OON, then it is 2-x from 600N. equate the moments from both ends. we get 400x = 600(2-x)..... solving u get x=1.2M

Raviteja Deekonda - 7 years, 2 months ago

i didn,t get it

Rahmat Islam - 7 years, 2 months ago

the plank should be perfectly horizontal to prevent motor from falling.it will be horizontal only if the moments of forces about the point where motor is placed are equal.

Suraj Bhosale - 7 years, 1 month ago
Krishna J
Apr 3, 2014

The solution to this problem lies in the principle of moments torque. Equal and opposite forces constitute a couple.In this situation,the forces in this situation are the forces applied by the 2 workers.For the motor to remain in equilibrium it should be at the center of gravity of the wooden board,thus preventing the motor from sliding.Otherwise it will constitute a couple and the the whole system rotates and therefore the motor slips towards one side.The torques should be equal, to prevent this. F1,F2->Forces applied T1,T2 ->torques l1,l2 ->distances from point of application of the 2 forces let l1=x l2=200-x T1=T2 F1 l1=F2 l2 400(x)=600(200-x) =>x=1.4m from the 400 newton foce!!! TADA!!!!! You have the answer!!!

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these ain't couple forces...these are pair forces

SulpHuric Acid - 7 years, 2 months ago
Anubhav Sharma
Apr 3, 2014

The best way to give answers in multiple choice questions is to try all the options.

But before that we need to know

The principle of lever is :

Load Arm ( or load distance) * Load = Effort Arm ( or Effort distance) * Effort

or, L * Ld = E * Ed

Note : Effort distance or Effort arm is the distance from the distance to fulcrum. 

        Load distance or Load arm is the distance from the distance to fulcrum.

In this case, we can consider any of the two forces exerted by any boy as effort and any as load.

If we try first, second and fourth option then the equation does not balances. So, the correct option is the third one.

According to the third option

or, 400 N * 1.2m = 600 N * 0.8m ( Since, the total distance is 2m. i.e. Ed + Ld = 2m. If one distance is 1.2 m then the other must be 0.8m)

So, the correct option is the third one.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

i only understand ur solution bro good

Qamar Raj - 7 years, 2 months ago

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Thank you very much sir !!

Anubhav Sharma - 7 years ago

I think It should be nearer to Powerfull man i.e 1.6 from Mordecai.. cause he is applying greater FOrce so to balance....it should be placed nearer to Mordecai..... ..if i m wrong...explain? plzzzzz

SulpHuric Acid - 7 years, 2 months ago

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I don't think so.

Look, at first you must know the main thing or the formula

which is also known as the principle of lever in this case.

Lever is a simple machine that consists of a long rigid bar with fulcrum fixed on bar.

Similarly, since it is a machine it must consist of load and effort.

LOAD is the force that we are trying to lift. ( L )

EFFORT is the applied force to lift the load. ( E )

The distance between fulcrum and load is called load arm or load distance ( Ld ).

The distance between fulcrum and effort is called effort arm or effort distance ( Ed ).

If you have understood these terms then the formula would be easy.

The question says "They were supposed to carry a heavy electric motor placed on a light board of length 2.00 m."

which means

that Ed + Ld = 2 m

or , Ld = 2 m - Ed

The principle of lever states that Load Arm ( or load distance) * Load = Effort Arm ( or Effort distance) * Effort L * Ld = E * Ed Here we do not know which child is Load and which child is Effort. So, we can consider any of the two forces exerted by any boy as effort and any as load.

If we consider your condition then

It should be 1.6 m from Mordecai.

The applied force by Mordecai is 600 N

Then it must be 0.4 m from Rigby as the total distance is 2 m.

The applied force of Rigby is 400 N.

Let's put all that in to the principle and see if it works or not.

L * Ld = E * Ed

1.6 m * 600 N = 2 m * 400 N

960 N m = 800 N m

which is NOT correct

So that' s not the answer.

To get the correct answer follow the steps.

L * Ld = E * Ed

400 N *( 2 m - Ed ) = 600 N * Ed

800 Nm - 400 N * Ed = 600 N * Ed

800 Nm - 400 N * Ed = 600 N * Ed

800 Nm = 600 N Ed + 400 N Ed

800 Nm = 1000 N Ed

Ed = (\fract{800 Nm}{1000 N}

Ed = 0.8 m

Now ,

once we know that Ed is 0.8 m then the other ( Ld ) must be 1.2 m as the Ld + Ed = 2 m as stated in the question

So, the correct option is the third one.

If you have still more confusion feel free to ask me.

Anubhav Sharma - 7 years ago

friend its quite simple. we just need to make sure that moment of forces are equal so that the plank does not rotate. moment of force= (force applied) x (vertical distance).

shuvam jaiswal - 7 years ago

i'm the most dumb person here ...can't even understand what the hell I have to fine :/

Tàkky Rajput - 7 years, 2 months ago

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Look, at first you must know the main thing or the formula

which is also known as the principle of lever in this case.

Lever is a simple machine that consists of a long rigid bar with fulcrum fixed on bar.

Similarly, since it is a machine it must consist of load and effort.

LOAD is the force that we are trying to lift. ( L )

EFFORT is the applied force to lift the load. ( E )

The distance between fulcrum and load is called load arm or load distance ( Ld ).

The distance between fulcrum and effort is called effort arm or effort distance ( Ed ).

If you have understood these terms then the formula would be easy.

The question says "They were supposed to carry a heavy electric motor placed on a light board of length 2.00 m."

which means

that Ed + Ld = 2 m

or , Ld = 2 m - Ed

The principle of lever states that

Load Arm ( or load distance) * Load = Effort Arm ( or Effort distance) * Effort

L * Ld = E * Ed

Here we do not know which child is Load and which child is Effort.

So, we can consider any of the two forces exerted by any boy as effort and any as load.

400 N *( 2 m - Ed ) = 600 N * Ed

800 Nm - 400 N * Ed = 600 N * Ed

800 Nm - 400 N * Ed = 600 N * Ed

800 Nm = 600 N Ed + 400 N Ed

800 Nm = 1000 N Ed

Ed = 800 N m 1000 N \frac{800 N m}{1000 N}

Ed = 0.8 m

Now ,

once we know that Ed is 0.8 m then the other ( Ld ) must be 1.2 m as the Ld + Ed = 2 m as stated in the question

So, the correct option is the third one.

Anubhav Sharma - 7 years ago

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If you are still confused then feel free to ask me more !!!!!

Anubhav Sharma - 7 years ago
Abhinav Kumar
Apr 2, 2014

Balance forces first. And then torque about the center of board.

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400/600=2/3 so distance should also be in the same ratio divide 2 mt in same proportion we get 0.8 mt and 1.2 mt

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Mubeen Chughtai
Apr 4, 2014

Let point mass is located at A having distance x from 400N force and 2-x from 600N. Taking moment at point A

400x=600(2-x)

400x=1200-600x

1000x=1200

X=1.2m

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Akib Nafis
Apr 3, 2014

very easy.just find the value of x from here 400 x=600 (2-x) [this is for finding the distance from Ri]

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I have a doubt, what I did is, The ratio of force is 400/600, that is 2/3. And the board is 2 meters in length. So, in order to attain equilibrium, I need to calculate two third of 2 right? (2/3)*2 which is 1.33, so the motor should be 1.33 meters away from Rigby or approximately 1.6 meters from the other person right? Where am I going wrong?

Puranik Shantharam - 7 years, 2 months ago

Hallo,

given that Mordecai is 600N weight, Rigby is 400N, the length of board is 2.0m,

as for centre of mass, let r1=distance of Mordecai from centre of mass, r2 = distance of Rigby from centre of mass,

by applying m1r1 = m2r2 , stated that they are applying upward forces , let N=upward force N=W,as w = mg...

600 / 9.81 r1 = 400 / 9.81 r2

r1 / r2 = 400 / 600

r1 / r2 = 2 / 3

r1 : r2 = 2 : 3 by looking at the distance ratio ,you can see that to balance up the centre of mass, 3/5 from 2m board must be away from Rigby or 2 / 5 from Mordecai,

as for Mordecai = 2/5 x 2.0 = 0.8m,

as for Rigby = 2.0m - 0.8m = 1.2m(or equivalent to 3/5 from 2.0),

therefore in the answer options , there's only distance from Rigby that is 1.2m away.....

thanks ahh.....

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