The total linear momentum of a system of five particles at time t=2.2 s is given by G22=3.4 i- 2

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The total linear momentum of a system of five particles at...

The total linear momentum of a system of five particles at time $t=2.2 \mathrm{s}$ is given by $\mathrm{G}_{22}=3.4 \mathrm{i}-$ $2.6 j+4.6 \mathrm{k} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s} .$ At time $t=2.4 \mathrm{s},$ the linear momentum has changed to $\mathbf{G}_{2,4}=3.7 \mathbf{i}-2.2 \mathbf{j}+4.9 \mathbf{k}$ $\mathrm{kg} \cdot \mathrm{m} / \mathrm{s} .$ Calculate the magnitude $F$ of the time average of the resultant of the external forces acting on the system during the interval.

The total linear momentum of a system of five particles at time $t=2.2 \mathrm{s}$ is given by $\mathrm{G}_{22}=3.4 \mathrm{i}-$ $2.6 j+4.6 \mathrm{k} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s} .$ At time $t=2.4 \mathrm{s},$ the linear momentum has changed to $\mathbf{G}_{2,4}=3.7 \mathbf{i}-2.2 \mathbf{j}+4.9 \mathbf{k}$
$\mathrm{kg} \cdot \mathrm{m} / \mathrm{s} .$ Calculate the magnitude $F$ of the time average of the resultant of the external forces acting on the system during the interval.

Key Concepts

Linear Momentum

Linear momentum is a conserved vector quantity for a system of particles, defined as the product of the total mass and the velocity of the center of mass of the system. It describes the quantity of motion the system possesses and is fundamental for analyzing collisions and interactions under external forces.

Impulse-Momentum Theorem

The impulse-momentum theorem states that the change in the linear momentum of a system is equal to the impulse applied to it. This relationship forms the basis for calculating the effect of forces acting over a finite time interval, linking force, time, and momentum change.

Resultant External Force

The resultant external force is the vector sum of all individual external forces acting on a system. According to Newton’s second law, this net force is responsible for the acceleration of the system's center of mass as it produces a change in the system's momentum.

Time Averaged Force

The time averaged force is calculated by dividing the total impulse (i.e., the change in momentum) by the time interval over which the force acted. It provides a simplified measure of the force's overall effect on the system during that period.

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