An internet shopping company is planning to use drones to deliver packages - Scottish Highers Physics - Question 2 - 2018

The power $P$ dissipated by the motor can be calculated using the formula:

$P = \frac{V^2}{R}$

where $V$ is the voltage and $R$ is the resistance.

Given that the battery supplies $V = 12 ext{ V}$ and the resistance of the motor is $R = 9 ext{ Ω}$, we substitute these values into the formula:

$P = \frac{12^2}{9} = \frac{144}{9} = 16 ext{ W}$

Therefore, the power dissipated by the motor is 16 W.

While the cable is being lowered and it breaks, the upward force produced by the drone remains constant as stated in the question. Since the upward force exceeds the weight of the package, it remains greater than the gravitational force acting on the package. This results in an unbalanced force acting upwards, causing the drone to accelerate upwards immediately after the cable breaks.

To find the tension in each cord, we can analyze the forces acting on the system.

Given that the mass of the package is 3.4 kg, we first calculate the total weight:

$W = mg = 3.4 imes 9.8 = 33.32 ext{ N}$

Assuming the tension is $T$ in each cord, and the system is balanced at a constant height, we can apply the trigonometric relation for the angle of 35°. The force components in the vertical direction yield:

$2T \times \sin(35°) = W$

Thus,

$2T \times \sin(35°) = 33.32$

Solving for $T$, we have:

$T = \frac{33.32}{2 \times \sin(35°)} = \frac{33.32}{2 \times 0.5736} \approx 29.06 ext{ N}$

Hence, the tension in each cord is approximately 29.06 N.