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A balanced lever has two weights on it, one with mass #2 kg# and one with mass #8 kg#. If the first weight is # 4 m# from the fulcrum, how far is the second weight from the fulcrum?

Answer 1

Elena Albarran

The distance is #=1m#

The mass #M_1=2kg#

The mass #M_2=8kg#

The distance #a=4m#

Taking moments about the fulcrum

#M_1xxa=M_2xxb#

The distance is

#b=(M_1xxa)/(M_2)=(2*4)/(8)=1m#

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Answer 2

Amelia Adams

#1m#

The concept that comes into use here is torque. For the lever to not tip over or rotate, it must have a net torque of zero.

Now, the formula of torque is #T=F*d#.

Take an example to understand, if we hold a stick and attach a weight at the front of the stick, it doesn't seem too heavy but if we move the weight to the end of the stick, it seems a lot heavier. This is because the torque increases.

Now for the torque to be same, #T_1=T_2#

#F_1*d_1=F_2*d_2#

The first block weighs 2 kg and exerts approximately #20N# of force and is at a distance of 4m

The first block weighs 8 kg and exerts approximately #80N#

Putting this in the formula,

#20*4=80*x#

We get that x= 1m and hence it must be placed at a distance of 1m

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Answer 3

Benjamin Asiedu

The second weight is 1 meter from the fulcrum.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.