A 0.54 kg particle has a speed of8.0 m/s at point A and kineticenergy of 7.5 J at point B. (a) What is its kinetic energy at A? J
(b) What is its speed at point B?m/s
(c) What is the total work done on the particle as it moves fromA to B? J

a) The translational kinetic energy of the particle at point A is 17.28 joules.

b) The speed of the particle at point B is approximately 5.270 meters per second.

c) The total work done on the particle as it moves from A to B is - 9.78 joules.

Explanation:

Let be this particle a conservative system, that is, that non-conservative forces (i.e. friction, viscosity) are negligible.

a) The translational kinetic energy of the particle (), measured in joules, is determined by the following formula:

(1)

Where:

- Mass, measured in kilograms.

- Speed, measured in meters per second.

If we know that and , the translational kinetic energy at point A is:

The translational kinetic energy of the particle at point A is 17.28 joules.

b) The speed of the particle is clear in (1):

If we know that and , then the speed of the particle at point B:

The speed of the particle at point B is approximately 5.270 meters per second.

c) According to the Work-Energy Theorem, the total work done on the particle as it moves from A to B (), measured in joules, is equal to the change in the translational kinetic energy of the particle. That is:

(2)

If we know that and , then the change in the translational kinetic energy of the particle is:

The total work done on the particle as it moves from A to B is - 9.78 joules.

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