A truck of mass 2.1 × 10³ kg tows a car of mass 1.3 × 10³ kg along a horizontal road - AQA - A-Level Physics - Question 24 - 2022 - Paper 1

Next, we must account for the total resistive forces acting on the car. Given that the total resistive force is 1100 N, the tension in the tow rope also needs to overcome this force for the car to accelerate. Thus, we summarize the forces acting on the car:

$T - F_{resistive} = m_{car} \times a$

Where:

$T$ = tension in the rope

$F_{resistive} = 1100 \, N$

$m_{car} = 1.3 \times 10^3 \, kg$

$a = 2.3 \, m/s^2$

Rearranging gives: $T = m_{car} \times a + F_{resistive}$

Substituting the known values:

$T = (1.3 \times 10^3 \times 2.3) + 1100$ $T = 2990 + 1100 = 4090 \, N$

Rounding to the nearest hundred, the tension in the tow rope is approximately 4100 N.