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A) Hooke's Law states that the extension of a spring is directly proportional to the force applied to it, provided the elastic limit is not exceeded.

Physics

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2 parts
b

20 N/m\text{20 N/m}

d(i)

Q=mLvQ = mL_v

Step-by-step solution

3 steps

Part a

Hooke's Law states that the extension of a spring is directly proportional to the force applied to it, provided the elastic limit is not exceeded.

Part b

20 N/m\text{20 N/m}

The proportionality constant of the spring, also known as the spring constant (kk), is given by the ratio of the applied load (force, FF) to the extension (xx).

k=Fxk = \frac{F}{x}
  1. Choose a point from the linear portion of the graph.

    From the graph, when the Load (FF) is 1 N1 \text{ N}, the Extension (xx) is 5 cm5 \text{ cm}.

  2. Convert the extension from centimeters to meters to use SI units for the spring constant.

    x=5 cm=0.05 mx = 5 \text{ cm} = 0.05 \text{ m}
  3. Calculate the spring constant kk.

    k=1 N0.05 m=20 N/mk = \frac{1 \text{ N}}{0.05 \text{ m}} = 20 \text{ N/m}

    Using another point, for example, when Load (FF) is 4 N4 \text{ N}, Extension (xx) is 20 cm20 \text{ cm}.

    x=20 cm=0.20 mx = 20 \text{ cm} = 0.20 \text{ m} k=4 N0.20 m=20 N/mk = \frac{4 \text{ N}}{0.20 \text{ m}} = 20 \text{ N/m}

    The proportionality constant of the spring is 20 N/m\boxed{\text{20 N/m}}.

Part c

Two factors that affect the proportionality constant of a vertical spring are

  • The material of the spring (e.g., steel, copper).
  • The diameter of the wire used to make the spring.

Part d(i)

Q=mLvQ = mL_v

Given that the LvL_v is the specific latent heat of vaporization of steam.

ii) The latent heat of vaporization (QQ) is the total energy required to change the state of a mass mm of a substance at its boiling point without a change in temperature. Given LvL_v is the specific latent heat of vaporization (energy per unit mass), the expression for the total latent heat of vaporization is:

Q=mLvQ = mL_v

where mm is the mass of the steam and LvL_v is the specific latent heat of vaporization.
The expression for the latent heat of vaporization of steam is Q=mLv\boxed{Q = mL_v}.

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