A crane is lifting an object of mass 600 kg from point A to point B at a CONSTANT SPEED to a vertical height of 25 m in two minutes, as shown in the diagram below - NSC Technical Sciences - Question 4 - 2023 - Paper 1

Power can be calculated using the formula:

P = rac{W}{t}

where:

• $W = 147000 ext{ J}$ (work done, calculated previously).
• $t = 120 ext{ s}$ (time taken, since 2 minutes = 120 seconds).

Now, substituting the values: P = rac{147000 ext{ J}}{120 ext{ s}} = 1225 ext{ W}

Thus, the power at which the crane operates is 1225 W.

Gravitational potential energy is the energy that an object possesses due to its position in a gravitational field. It is the work done against gravity to lift an object to a certain height.

The kinetic energy (KE) of an object can be calculated using the formula:

KE = rac{1}{2} m v^2

where:

• $m = 3 ext{ kg}$ (mass of the brick).
• $v = 7 ext{ m/s}$ (velocity just before hitting the ground).

Substituting the values: KE = rac{1}{2} imes 3 ext{ kg} imes (7 ext{ m/s})^2 = rac{1}{2} imes 3 imes 49 = 73.5 ext{ J}

Thus, the kinetic energy of the brick just before it hits the ground is 73.5 J.

We can use the conservation of energy principle: the potential energy at the height of the drop is converted to kinetic energy just before the brick hits the ground.

The formula for potential energy is:

$PE = mgh$

Setting the potential energy equal to the kinetic energy: $mgh = KE$

Substituting the values:

• $m = 3 ext{ kg}$
• $g = 9.8 ext{ m/s}^2$
• $KE = 73.5 ext{ J}$

We can solve for height (h): $3 imes 9.8 imes h = 73.5$

Rearranging: h = rac{73.5}{3 imes 9.8} = rac{73.5}{29.4} = 2.5 ext{ m}

Thus, the height from which the brick was dropped is 2.5 m.