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 states: "An object will remain at rest or in uniform motion in a straight line unless acted upon by a net external force."

In the free-body diagram for the car, the following forces should be represented: the weight (gravity) acting downwards, the normal force acting upwards, the tension in the rope pulling towards the caravan, and the applied force (if any) acting in the same direction as the tension. Make sure to label each force appropriately.

To calculate the acceleration of the system, the net force acting on the whole system comprising the car and the caravan must be calculated. The total mass of the caravan and car combined is:

$m_{ ext{total}} = 1300 ext{ kg} + 900 ext{ kg} = 2200 ext{ kg}$

The resultant force acting on the system is the force exerted by the car:

$F_{ ext{net}} = 10500 ext{ N}$

Thus, using Newton's second law, we can find the acceleration:

$a = \frac{F_{ ext{net}}}{m_{ ext{total}}} = \frac{10500 ext{ N}}{2200 ext{ kg}} = 4.77 ext{ m/s}² \text{ to the right}$

Using the acceleration calculated above, we can find the tension in the rope. The tension can be calculated for the caravan using:

$F_{ ext{net}} = m_{ ext{caravan}} imes a$

So we have:

$T = 900 ext{ kg} imes 4.77 ext{ m/s}² = 4293 ext{ N}$

To find the resultant force acting on the falling elevator, we detail the forces: the gravitational force (weight) and the retarding force from the guide rails. The weight is calculated as:

$w = m imes g = 1600 ext{ kg} imes 9.8 ext{ m/s}² = 15680 ext{ N}$

Now, the resultant force is:

$F_{ ext{net}} = w - F_{ ext{retard}} = 15680 ext{ N} - 3700 ext{ N} = 11980 ext{ N} \text{ downwards}$

Using Newton's second law, the acceleration can be calculated as:

$a = \frac{F_{ ext{net}}}{m} = \frac{11980 ext{ N}}{1600 ext{ kg}} = 7.49 ext{ m/s}² \text{ downwards}$

Newton's Third Law states that: "For every action, there is an equal and opposite reaction." This means that when one object exerts a force on another, the second object exerts a force of equal magnitude in the opposite direction back onto the first object.

When the apple falls, the action force is the weight of the apple acting downward due to gravity. The corresponding reaction force is the force that the apple exerts upward on the Earth. Thus, these forces are equal in magnitude and opposite in direction.