Question

If a car can accelerate at 4m/sec2, what acceleration can it attain if it is pulling another car of identical mass?

Answer 1

Answer on Question #42250 – Physics – Mechanics | Kinematics | Dynamics

If a car can accelerate at $4\mathrm{m}/\mathrm{sec}^2$, what acceleration can it attain if it is pulling another car of identical mass?

Solution:

$a = 4 \frac{\mathrm{m}}{\mathrm{s}^2} -$ initial acceleration of the car;

$a_1$ – acceleration of the car while pulling another car if identical mass;

Second Newton's law in projections on X-axis, assuming a car moves along a horizontal road:

$$F - kN = ma$$

where $F$ is the pulling force of the engine, $kN$ is the friction force (k is the friction coefficient). The normal force can be found, noting that it is compensated by the gravity force:

$$N = mg.$$

So, the acceleration is

$$a = \frac{F}{m} - gk$$

If the car pulls another car of identical mass, that the second Newton for these cars law must be written as

$$\left\{ \begin{array}{l} F - kN - T = ma_1 \\ T - kN = ma_1 \end{array} \right.$$

where $T$ is the tension force of the rope and $N = mg$ for each car.

As one can solve, the resulting acceleration becomes $a_1 = \frac{F}{2m} - gk$. So,

$$a_1 = a - \frac{F}{2m}$$

Hence, acceleration $a_1$ depends on the pulling force of the engine and the mass of a car.

Answer: $a_1 = a - \frac{F}{2m}$ where $F$ is the pulling force of the engine and $m$ is the mass of the car.

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