Question

A car and a truck have the same kinetic energies at a certain instant while they are moving along two parallel roads. Which one will have greater momentum? 



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Answer 1

Explanation:

Work done =Force×distance= Change in kinetic energy. Both the truck and the car had same kinetic energy and hence same amount of work is needed to be done. As retarding force applied is same for both, therefore, both the truck and the car travel the same distance before coming to rest.

Answer 2

Answer:

The momentum of the truck will be more than the momentum of the car.

Explanation:

Let, the kinetic energy of the car be $\frac{1}{2} mv_1^2$

where, $m$ is the mass of the car,

$v_1$ is the velocity of the car.

Let, the kinetic energy of the truck be $\frac{1}{2} Mv_2^2$

where, $M$ is the mass of the truck,

$v_2$ is the velocity of the truck.

Given: Kinetic energies of the car and the truck are equal.

equating both kinetic energies,

$\frac{1}{2} mv_1^2=\frac{1}{2} Mv_2^2$

$\implies mv_1^2= Mv_2^2$

$\implies \frac{m}{m}* mv_1^2= \frac{M}{M}* Mv_2^2$

$\implies \frac{m^2v_1^2}{m}= \frac{M^2v_2^2}{M}$

The general formula of momentum: $p=mv$

$\implies \frac{p_1^2}{m}= \frac{p_2^2}{M}$         [$p_1, p_2$ are respective momentum of car and the truck]

$\implies \frac{p_1^2}{p_2^2}= \frac{m}{M}$

$\implies \frac{p_1}{p_2}= \sqrt{\frac{m}{M}}$

The ratio of the momentum of car and truck is :   $p_1:p_2=\sqrt{m} :\sqrt{M}$

As the mass of the truck($M$) is more than car's($m$), $\implies$ $p_2 > p_1$

So, the momentum of the truck will be more than the momentum of the car.

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