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-g Two people carry a heavy electric motor by placing it on a light board 2.00 m long. One person lifts at one end with a force of 400 N, and the other lifts the opposite end with a force of 600 N. (a) What is the weight of the motor, and where along the board is its center of gravity located

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Answer:

(A) 1000 N

(B) 1.2 m from the 400 N force

Explanation:

length of the board (R) = 2 m

force at one end (F1) = 400 N

force at other end (F2) = 600 N

let the distance of force F1 from the motor be = r

let the distance of force F2 from the motor be = r

therefore r + r' = 2 m

(A) what is the weight of the motor?

    since the system is in equilibrium, the weight of the motor will be equal to the force applied by the two persons to lift the motor. therefore

weight of the motor = 600 + 400 = 1000 N

(B) where along the board is the center of gravity located?

 since the system is in equilibrium, the summation of the torque exerted by the 400 N (F1) will be equal to the torque exerted by the 600 N (F2)

torque exerted by the 400 N (F1) = torque exerted by the 600 N (F2)

 F1 x r = F2 x r'

  • recall that r + r' = 2
  • r' = 2 - r
  • now substituting r' = 2 -r into the equation

 F1 x r = F2 x (2 - r)

  • substituting the values of F1 and F2 we have

400r = 600(2-r)

400r = 1200 - 600r

400r + 600r = 1200

 1000r = 1200

  r = 1200/1000

  r = 1.2 m

therefore the motor is 1.2 m from the 400 N force

(A) The weight of the motor should be considered as the 1000 N.

(B) It should be located like 1.2 m from the 400 N force.

Calculation of the weight:

Since

length of the board (R) = 2 m

force at one end (F1) = 400 N

force at other end (F2) = 600 N

Here we assume following things

let the distance of force F1 from the motor be = r

let the distance of force F2 from the motor be = r

So, r + r' = 2 m

a. here the weight should be

= 600 + 400

= 1000 N

b.

Since

F1 x r = F2 x r'

So,

here we have to recall that r + r' = 2

r' = 2 - r

now substituting r' = 2 -r into the equation

F1 x r = F2 x (2 - r)

So,

400r = 600(2-r)

400r = 1200 - 600r

400r + 600r = 1200

1000r = 1200

 r = 1200/1000

 r = 1.2 m

Learn more about gravity here: https://brainly.com/question/17384612

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