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 #42225 – Physics – Mechanics | Kinematics | Dynamics

1. 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?

$$a = 4 \frac{m}{s^2}$$ $$a_1 - ?$$

Solution.

Let write the second Newton law in projections on $X$-axis, assuming a car moves along a horizontal road:

$$ma = F - \mu N,$$

where $F$ is the pulling force of the engine, $\mu N$ is the friction force ($\mu$ 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

$$a = \frac{F}{m} - \mu g.$$

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

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

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

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

This acceleration 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 $a_1 = a - \frac{F}{2m}$ is the mass of a car.

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