If the length of a #37 cm# spring increases to #73 cm# when a #4 kg# weight is hanging from it, what is the spring's constant?
The spring constant is
The mass is The extension is The spring constant is
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To find the spring constant, you can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The formula for Hooke's Law is:
[ F = k \cdot x ]
Where:
- ( F ) is the force exerted by the spring (in Newtons)
- ( k ) is the spring constant (in Newtons per meter)
- ( x ) is the displacement from the equilibrium position (in meters)
Given that the spring's length increases from 37 cm to 73 cm when a 4 kg weight is hanging from it, the displacement (( x )) is the difference between the two lengths, converted to meters.
[ x = (73 - 37) , \text{cm} = 36 , \text{cm} = 0.36 , \text{m} ]
Now, we can use Hooke's Law to find the spring constant (( k )). We need to calculate the force exerted by the weight, which is equal to the weight of the object (mass multiplied by gravity).
[ F = m \cdot g ]
Given:
- ( m = 4 , \text{kg} ) (mass of the weight)
- ( g = 9.81 , \text{m/s}^2 ) (acceleration due to gravity)
[ F = 4 \times 9.81 , \text{N/kg} = 39.24 , \text{N} ]
Now, we can use Hooke's Law to find the spring constant (( k )):
[ k = \frac{F}{x} ]
Substitute the values: [ k = \frac{39.24}{0.36} ]
[ k \approx 109 , \text{N/m} ]
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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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