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Two pucks are initially moving along a frictionless surface as shown in the diagram. The pucks have mass $m_{1} < m_{2}$ and begin with equal magnitude of momentum. A constant force $F$ is applied to each puck directly to the right for the same amount of non-zero time. After the pushes are complete, what is the relationship for the size of the momenta of pucks ( $p_{1} a n d p_{2}$ ) ?

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$p_{1} < p_{2}$

$p_{1} = p_{2}$

$p_{1} > p_{2}$

More information about the masses, speeds, force and time are required to answer the questions

answer is A.

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Detailed Solution

${\vec{F}}_{e x t} = \frac{d \vec{P}}{d t} \Rightarrow \vec{F t} = \vec{P}$

now final

$\vec{P_{f}} = {\vec{P}}_{i} + ∆ \vec{P} |\vec{P_{f}}| = \sqrt{{P_{i}}^{2} + {(∆ P)}^{2} + 2 P_{i} ∆ P \cos θ}$

When $θ$ is the angle between $∆ \vec{P} a n d \vec{P_{i}}$

Since this angle is less for puck 2

$P_{f}$ for 2 is greater

Hence $p_{1} < p_{2}$

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