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The velocity ratio (VR) of a machine is defined as the ratio of the distance moved by the effort to the distance moved by the load.

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2 parts
b(i)

600 J\text{600 J}

b(ii)

750 J\text{750 J}

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Here are the solutions to the questions:

Part a

The velocity ratio (VR) of a machine is defined as the ratio of the distance moved by the effort to the distance moved by the load.

Velocity Ratio=Distance moved by effortDistance moved by load\text{Velocity Ratio} = \frac{\text{Distance moved by effort}}{\text{Distance moved by load}}

Part b(i)

600 J\text{600 J}

The work done on the load

Given:
Mass of load, m=20 kgm = 20 \, \text{kg}
Effort force, F=150 NF = 150 \, \text{N}
Vertical height, h=3 mh = 3 \, \text{m}
Length of inclined plane (distance moved by effort), L=5 mL = 5 \, \text{m}
Acceleration due to gravity, g=10 m/s2g = 10 \, \text{m/s}^2 (assumed)

  1. Calculate the weight of the load.

    The weight of the load is the force of gravity acting on it.

    Weight=m×g\text{Weight} = m \times g Weight=20 kg×10 m/s2\text{Weight} = 20 \, \text{kg} \times 10 \, \text{m/s}^2 Weight=200 N\text{Weight} = 200 \, \text{N}

  2. Calculate the work done on the load.

    Work done on the load is the product of its weight and the vertical height it is lifted.

    Wload=Weight×hW_{\text{load}} = \text{Weight} \times h Wload=200 N×3 mW_{\text{load}} = 200 \, \text{N} \times 3 \, \text{m} Wload=600 JW_{\text{load}} = 600 \, \text{J}

    The work done on the load is 600 J\boxed{\text{600 J}}.

Part b(ii)

750 J\text{750 J}

Work done by the effort

  1. Identify the effort force and the distance moved by the effort.

    Effort force, F=150 NF = 150 \, \text{N}
    Distance moved by effort (length of the inclined plane), L=5 mL = 5 \, \text{m}

  2. Calculate the work done by the effort.

    Work done by the effort is the product of the effort force and the distance it moves.

    Weffort=F×LW_{\text{effort}} = F \times L Weffort=150 N×5 mW_{\text{effort}} = 150 \, \text{N} \times 5 \, \text{m} Weffort=750 JW_{\text{effort}} = 750 \, \text{J}

    The work done by the effort is 750 J\boxed{\text{750 J}}.

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