Question

Explain two scenarios where a large truck can have the same momentum as a small car.

Answer 1

The momentum, p, of any object having mass m and the velocity v is

$p=mv\cdots(i)$

Let $M_L$ and $M_S$ be the masses of the large truck and the car respectively, and $V_L$ and V_S be the velocities of the large truck and the car respectively.

So, by using equation (i),

the momentum of the large truck $= M_LV_L$

and the momentum of the small car $= M_SV_S$.

If the large truck has the same momentum as a small car, then the condition is

$M_LV_L=M_SV_S\cdots(ii)$

The equation (ii) can be rearranged as

$\frac {M_L}{M_S}=\frac {V_S}{V_L} \; or \; \frac{M_L}{V_S}=\frac{M_S}{V_L}$

So, the first scenario:

$\frac {M_L}{M_S}=\frac {V_S}{V_L}$

$\Rhghtarrow M_L:M_S=V_S:V_L$

So, to have the same momentum, the ratio of mass of truck to the mass of the car must be equal to the ratio of velocity of the car to the velocity of the truck.

The other scenario:

$\frac{M_L}{V_S}=\frac{M_S}{V_L}$

$\Rhghtarrow M_L:V_S= M_S:V_L$

So, to have the same momentum, the ratio of mass of truck to the velocity of the car must be equal to the ratio of mass of the car to the velocity of the truck.