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?

Answer 1

The spring constant is #=108.9nm^-1#

The mass is #=4kg#

The extension is #Deltax=0.73-0.37=0.36m#

The spring constant is

#k=F/(Deltax)=4g/0.36=108.9Nm^-1#

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Answer 2

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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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.

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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