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Zorluk: OrtaNewton's Laws of Motion and Linear Momentum

When a stationary object in an isolated system explodes into two fragments of unequal mass, the fragment with the larger mass acquires a greater magnitude of linear momentum than the fragment with the smaller mass.

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The statement is false. Both fragments acquire linear momentum of equal magnitude in opposite directions.
The statement is false because conservation of linear momentum requires the total initial momentum (zero) to equal the total final momentum. Therefore, the two fragments move in opposite directions with linear momenta of equal magnitude, regardless of their masses.

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1
Analyze internal forces acting during the explosion
By Newton's third law, the force exerted on the first fragment is equal in magnitude and opposite in direction to the force exerted on the second fragment (F1=−F2F_1 = -F_2).
Explosive forces are internal action-reaction pairs.
2
Apply the impulse-momentum theorem
Since both forces act for the exact same duration Δt\Delta t, the impulse J1=F1ΔtJ_1 = F_1 \Delta t equals −J2=−F2Δt-J_2 = -F_2 \Delta t. Therefore, the change in linear momentum Δp1=−Δp2\Delta p_1 = -\Delta p_2.
Impulse delivered to an object equals its change in linear momentum.
3
Compare momentum magnitudes
∣p1∣=∣p2∣|p_1| = |p_2|, which means m1v1=m2v2m_1 v_1 = m_2 v_2.
Initial momentum was zero (pinitial=0p_{\text{initial}} = 0), so the sum of final momentum vectors must be zero (p1+p2=0p_1 + p_2 = 0).

Anahtar Kavram

Conservation of Linear Momentum and Newton's Third Law
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Konular

Newton's Laws of Motion and Linear Momentum

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