Question

A lever of first order has a total length of 3 m and is able to lift a load of 60 N with a force of 30 N. Find the position of the fulcrum.

Step by step answer is requested

Answer 1

$\large{\bf{ \underline{ \underline{Answer : }}}}$

• The position of the fulcrum is 1 m from the load.

Given :

• Load of the liver = 60 N
• Effort of the liver = 30 N

To Find :

• The position of the fulcrum from the load.

Calculation :

Let's assume the position of the fulcrum from the load as 'x'

• So, Effort arm will be (3 - x)

As we know that,

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• $\boxed{ \pmb{ \rm{ \red{Load \times Load \: arm = Effort \times Effort \: arm }}}}$

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Putting the values,

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$\longrightarrow \sf \: 60 \times x = 90 - 30x \\ \\ \\ \longrightarrow \sf \: 60 x = 90 - 30x \\ \\ \\ \longrightarrow \sf \: 90x = 90 \\ \\ \\ \longrightarrow \sf \: x = \cancel\dfrac{90}{90} \\ \\ \\ \longrightarrow { \boxed{\sf x = 1 \: m}} \: \pink{ \bigstar}$

Therefore, the position of the fulcrum is 1 m from the load.

Answer 2

Given :-

• Load of the liver = 60 N
• Effort of the liver = 30 N

To find :-

• Find the position of the fulcrum from the load ?

★ $\large\underline{\frak{As~we~know~that,}}$

$\large\dag$ Formula Used :

• $\boxed{\bf{Load~×~Load~arm~=~Effort~×~Effort~arm}}[\tex] [tex]\large\star$

Solution :-

Let's assume the position of the fulcrum from the load as ' x '.

• Now, Effort arm will be (3 - x)

Substituting the values :

:$\implies$ 60 × x = 90 - 30x

$~~~~~$:$\implies$ 60x = 90 - 30x

$~~~~~~~~~~$:$\implies$ 90x = 90

$~~~~~~~~~~~~~~~$:$\implies$ x = $\large\sf{\cancel{\frac{90}{90}}}$

$~~~~~~~~~~~~~~~~~~~~$:$\implies$${\underline{\boxed{\pink{\frak{x~=~1~m}}}}}$★

$\large\dag$ Hence Verified,

• The position of the fulcrum is $\large\underline{\sf{1~m}}$ from the load.