4.1 Define work done. 4.1.2 Calculate the work done by the applied force over the 8 m. 4.2 A construction worker of mass 75 kg is airlifted vertically upwards from a construction site, as shown in the diagram below. The worker is lifted, from the first floor of a building by a cable to a height of 12 m at a constant speed of 3 m s⁻¹. (Ignore air friction and assume that there is NO sideways motion.) 4.2.1 State the principle of conservation of mechanical energy in words. 4.2.2 Calculate the potential energy gained by the construction worker 12 metres above the first floor. 4.2.3 Calculate his kinetic energy as he was lifted for 12 m. 4.3 The total mechanical energy of the construction worker at the highest point is 11 500 J. Determine the potential energy of the construction worker just before he was airlifted by the helicopter.

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4.1 Define work done - NSC Technical Sciences - Question 4 - 2021 - Paper 1

Question 4

4.1 Define work done. 4.1.2 Calculate the work done by the applied force over the 8 m. 4.2 A construction worker of mass 75 kg is airlifted vertically upwards from... show full transcript

Worked Solution & Example Answer:4.1 Define work done - NSC Technical Sciences - Question 4 - 2021 - Paper 1

Step 1

Define work done.

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Answer

Work done is defined as the product of the force applied on an object and the displacement in the direction of the force. Mathematically, it can be expressed as:

$W = F imes d imes ext{cos}( heta)$

where:

$W$ is the work done,
$F$ is the applied force,
$d$ is the distance moved by the object,
$heta$ is the angle between the force and the direction of motion.

Step 2

Calculate the work done by the applied force over the 8 m.

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Answer

To find the work done, we can use the formula:

$W = F imes d imes ext{cos}( heta)$

Here,

$F = 60 ext{ N}$ ,
$d = 8 ext{ m}$ ,
$heta = 25^ ext{o}$ .

Calculating this gives:

$W = 60 imes 8 imes ext{cos}(25^ ext{o})$ $W ext{ (approximately) } = 60 imes 8 imes 0.9063 = 435.03 ext{ J}$

Step 3

State the principle of conservation of mechanical energy in words.

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Answer

The principle of conservation of mechanical energy states that in an isolated system, the total mechanical energy, which is the sum of potential energy and kinetic energy, remains constant, provided that no external forces do work on the system.

Step 4

Calculate the potential energy gained by the construction worker 12 metres above the first floor.

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Answer

The potential energy gained by the worker can be calculated using the formula:

$E_p = mgh$

where:

$m = 75 ext{ kg}$ ,
$g = 9.8 ext{ m/s}^2$ (acceleration due to gravity),
$h = 12 ext{ m}$ .

Therefore,

$E_p = 75 imes 9.8 imes 12 = 8,820 ext{ J}$

Step 5

Calculate his kinetic energy as he was lifted for 12 m.

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Answer

The kinetic energy can be determined using the formula:

$E_k = rac{1}{2} mv^2$

where:

$m = 75 ext{ kg}$ ,
$v = 3 ext{ m/s}$ (constant speed).

Thus,

$E_k = rac{1}{2} imes 75 imes (3)^2 = 0.5 imes 75 imes 9 = 337.5 ext{ J}$

Step 6

Determine the potential energy of the construction worker just before he was airlifted by the helicopter.

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Answer

The total mechanical energy at the highest point is given as 11,500 J. The potential energy at that point is already calculated as 8,820 J. Therefore, we can find the initial potential energy before being airlifted using:

$E_{total} = E_p + E_k$

Rearranging gives us:

$E_{p,before} = E_{total} - E_k$

Substituting in the values:

$E_{p,before} = 11,500 - 337.5 = 11,162.5 ext{ J}$

4.1 Define work done - NSC Technical Sciences - Question 4 - 2021 - Paper 1

Worked Solution & Example Answer:4.1 Define work done - NSC Technical Sciences - Question 4 - 2021 - Paper 1

Define work done.

Calculate the work done by the applied force over the 8 m.

State the principle of conservation of mechanical energy in words.

Calculate the potential energy gained by the construction worker 12 metres above the first floor.

Calculate his kinetic energy as he was lifted for 12 m.

Determine the potential energy of the construction worker just before he was airlifted by the helicopter.

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