Identical constant forces push two identical objects $A$ and $B$ continuously from a starting line to a finish line. If $A$ is initially at rest and B is initially moving to the right.

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Object A has the larger change in momentum

Object B has the larger change in momentum

Both objects have the same change in momentum

Not enough information is given to decide

answer is A.

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Detailed Solution

$m_{A} = m_{B} w_{F} = Δ k_{A} = Δ k_{B} p = \sqrt{2 mk} p_{f}^{2} - p_{i}^{2} = 2 m Δ k same for both \Rightarrow (p_{f} - p_{i}) (p_{f} - p_{i} + 2 p_{i}) is same for both Δ p (Δ p + 2 p_{i}) is same for both Δ p_{A} (Δ p_{A} + O) = Δ p_{B} (Δ p_{B} + 2 p_{i}) Δ p_{A} {}^{2}= Δ p_{B}^{2} + 2 (Δ p_{B}) p_{i} Δ p_{A} > Δ p_{B}$