Learners conduct an experiment to determine how the initial kinetic energy given to a trolley affects the distance the trolley moves on a rough horizontal surface - NSC Physical Sciences - Question 5 - 2023 - Paper 1

The independent variable in this experiment is the initial kinetic energy (E_{kA}) given to the trolley at point A.

The work-energy theorem states that the work done on an object by the net force acting on it is equal to the change in the object's kinetic energy. This can be formulated as: $W_{net} = riangle KE = KE_{final} - KE_{initial}$

To calculate the mass of the trolley, we start by using the relationship between the forces acting on it. The frictional force can be equated to the product of the coefficient of kinetic friction and the normal force:

1. Setting Up Equations:

   • The frictional force: $F_f = ext{μ}_k N = ext{μ}_k (mg)$, where $N = mg$.
   • At the point of rest, all kinetic energy has been converted into work done against friction.

2. Applying the Work-Energy Principle:

   • Assuming the distance traveled (Δx) is known, we apply: $W_{f} = F_f imes Δx = (0.18)(mg)Δx$.
   • Setting the work done equal to the initial kinetic energy gives: $E_{ki} = (0.18)(m)(9.8)(Δx)$

3. Calculating the Mass:

   • Using the specific Δx value from the experiment, rearranging for mass provides: m = rac{E_{ki}}{(0.18)(9.8)(Δx)}

4. Plugging in Values:

   • For example, if Δx is known from the graph, substitute this value to find the mass.