A mass of 1kg is acted upon a single force F =(4hat{i} + 4 hat{j})N . Due to this force, the...

Question:

A mass of 1kg is acted upon a single force {eq}F =(4\hat{i} + 4 \hat{j})N {/eq}. Due to this force, the mass is displaced from {eq}(0,0) {/eq} to {eq}(1m,1m) {/eq}. If initially the speed of the particle {eq}2m/s {/eq}, Its final speed should approximately be?

Work-Energy Theorem:

According to the work-energy theorem, the work done on the system is generally stored as the kinetic energy of the system. The work done is given by the dor product of the force and the displacement of the object.

Answer and Explanation:

Given data

Force on the object {eq}(F) = 4 \hat{i} + 4 \hat{j} \ N {/eq}

Now the displacement {eq}(r) = (1-0)\hat{i} + (1-0)\hat{j} \ m {/eq}

Initial speed of the mass {eq}(u) = 2 \ m/s {/eq}

Now, the work done will be equal to the change in the kinetic energy, therefore

{eq}F \cdot r = \dfrac{1}{2}m(v^{2} - u^{2})\\ (4 \hat{i} + 4 \hat{j}) \cdot (1 \hat{i} + 1\hat{j}) = \dfrac{1}{2}(1)(v^{2} - 2^{2})\\ v = 4.472 \ m/s {/eq}

where

  • v is the final velocity of the mass
  • m is the mass

Learn more about this topic:

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