A balanced lever has two weights on it, the first with mass #6 kg # and the second with mass #7 kg#. If the first weight is # 5 m# from the fulcrum, how far is the second weight from the fulcrum?
The distance is
The load The distance of the load from the fulcrum is The effort is The distance of the effort to the fulcrum is In a situation of equilibrium, the moments are equal So,
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To find the distance of the second weight from the fulcrum, we can use the principle of moments, which states that the sum of the anticlockwise moments is equal to the sum of the clockwise moments.
The moment (or torque) of a force about a point is given by the product of the force and the perpendicular distance from the point to the line of action of the force.
Let's denote:
- ( W_1 ) as the weight of the first mass (6 kg),
- ( W_2 ) as the weight of the second mass (7 kg),
- ( d_1 ) as the distance of the first weight from the fulcrum (5 m), and
- ( d_2 ) as the distance of the second weight from the fulcrum (which we need to find).
The moments exerted by each weight are equal, so we have:
[ W_1 \times d_1 = W_2 \times d_2 ]
Substituting the given values:
[ 6 \times 5 = 7 \times d_2 ]
Now, we can solve for ( d_2 ):
[ d_2 = \frac{6 \times 5}{7} ]
[ d_2 = \frac{30}{7} ]
Thus, the distance of the second weight from the fulcrum is ( \frac{30}{7} ) meters.
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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.
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.
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.
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.
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