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Calculate the work done against gravity and the work done by an applied force when moving a trolley up a slope.

Physics

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2 parts
a

3000 J\text{3000 J}

b

3863 J\text{3863 J}

Step-by-step solution

7 steps

Here are the solutions to question 12:

Part a· 3 steps

What is the work done on the trolley against the gravitational force in moving from A to B?

  1. Identify the given values.

    Mass of trolley, m=30 kgm = 30 \text{ kg}
    Vertical height gained, h=10 mh = 10 \text{ m}
    Acceleration due to gravity, g=10 m/s2g = 10 \text{ m/s}^2 (assuming this standard approximation)

  2. Use the formula for work done against gravity (change in gravitational potential energy).

    Wg=mghW_g = mgh
  3. Substitute the values and calculate.

    Wg=(30 kg)×(10 m/s2)×(10 m)W_g = (30 \text{ kg}) \times (10 \text{ m/s}^2) \times (10 \text{ m}) Wg=3000 JW_g = 3000 \text{ J}

    The work done against the gravitational force is 3000 J\boxed{\text{3000 J}}.

Part b

3863 J\text{3863 J}

Determine the work done by the force in moving the trolley from A to B.

  1. Identify the given values.

    Applied force, F=100 NF = 100 \text{ N} (parallel to the slope)
    Vertical height, h=10 mh = 10 \text{ m}
    Angle of inclination, θ=15∘\theta = 15^\circ

  2. Calculate the distance moved along the slope (dd).

    We use trigonometry: sin⁡(θ)=oppositehypotenuse=hd\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{d}
    So, d=hsin⁡(θ)d = \frac{h}{\sin(\theta)}

    d=10 msin⁡(15∘)d = \frac{10 \text{ m}}{\sin(15^\circ)} d≈10 m0.2588d \approx \frac{10 \text{ m}}{0.2588} d≈38.63 md \approx 38.63 \text{ m}
  3. Use the formula for work done by a force acting parallel to the displacement.

    WF=F×dW_F = F \times d
  4. Substitute the values and calculate.

    WF=(100 N)×(38.63 m)W_F = (100 \text{ N}) \times (38.63 \text{ m}) WF≈3863 JW_F \approx 3863 \text{ J}

    The work done by the force is 3863 J\boxed{\text{3863 J}}.

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