Passengers sitting in a bus observe that they move forward when the bus slows down to a stop and that they move backward when it accelerates from rest - NSC Technical Sciences - Question 2 - 2023 - Paper 1

The principle applied is Newton's First Law of Motion, which can be stated as: "An object will remain at rest or move in a straight line at a constant speed unless acted upon by a non-zero resultant force."

In the free-body diagram of the car, the following forces should be included:

• Weight (W): directed downward due to gravity.
• Normal Force (N): directed upward, balancing the weight.
• Tension (T): directed towards the caravan, pulling the car forward.
• Net Force (F_{Net}): resulting from T and any other horizontal forces acting on the car.

To find the acceleration of the system, we first calculate the net force acting on the system:

The total mass of the system = mass of the caravan + mass of the car = 900 kg + 1300 kg = 2200 kg.

Using Newton's second law, $F_{Net} = ma$, where $F_{Net} = 10,500 ext{ N}$ (pushing force), we have: $a = \frac{F_{Net}}{m} = \frac{10,500 ext{ N}}{2200 ext{ kg}} \approx 4.77 ext{ m/s}^2$

Using Newton's Second Law, we can find the tension in the rope by analyzing the caravan:

The net force on the caravan is given by: $F_{Net} = ma$, where $m = 900 ext{ kg}$ and $a = 4.77 ext{ m/s}^2$.

Thus, we have: $F_{Net} = 900 ext{ kg} \times 4.77 ext{ m/s}^2 = 4293 ext{ N}$.

The tension (T) in the rope supporting the caravan will balance this net force and any additional force from the car. For the car, the net upward force should be: $T - 10,500 ext{ N} = 0$, leading to: $T = 10,500 ext{ N} - 4293 ext{ N} \approx 6207 ext{ N}$.

To calculate the resultant force on the falling elevator, we must account for both the weight of the elevator and the retarding force:

Weight of the elevator: $w = mg = 1600 ext{ kg} \times 9.8 ext{ m/s}^2 = 15680 ext{ N}$

The net force acting on the elevator while falling is: $F_{Net} = w - F_{retarding} = 15680 ext{ N} - 3700 ext{ N} = 11980 ext{ N}$ downwards.

Using Newton's Second Law: $F_{Net} = ma$ We find the acceleration of the elevator: $a = \frac{F_{Net}}{m} = \frac{11980 ext{ N}}{1600 ext{ kg}} \approx 7.49 ext{ m/s}^2$ downwards.

Newton's Third Law states that for every action, there is an equal and opposite reaction. This means that forces exist in pairs, where one body exerts a force on another, and that second body simultaneously exerts a force of equal magnitude and opposite direction on the first body.

When the apple falls, the action force is the gravitational pull of the earth on the apple. The reaction force is the apple's gravitational pull on the Earth. Both forces are equal in magnitude but opposite in direction.