B4-WWT03: OBJECT CHANGING VELOCITY-WORK A 2-kg object accelerates as a net force acts on it.
During the 5 seconds this force acts, the object
changes its velocity from 3 m/s east to 7 m/s west.
A student states:
"The initial kinetic energy of the object was 9 Joules, and the final kinetic energy was 49 Joules. Thus the change in
kinetic energy of this object during these 5 seconds was 40 J, and thus the work done on this object by the net force
during this period was also 40 J.
What if anything, is wrong with this statement? If something is wrong, identify it and explain how to correct
it. If this statement is correct, explain why.

Part A;

The mass of the object, m = 2 kg

The initial velocity of the object, u = 3 m/s east

The final velocity of the object, v = 7 m/s west

The initial kinetic energy of the object =

The final kinetic energy of the object =

Based on the change in the momentum produced by the force which changes the direction  of the object, we add the two energy quantities to get the total change in energy as follows;

The change in kinetic energy =

The statement is wrong because the change in momentum brought about by the force should be included when finding the the total change in kinetic energy of the object during the 5 seconds period.

Part B;

The kinetic energy, K. E. = 1/2 × m × v²

The kinetic energy of the car A =

The kinetic energy of the car B =

The kinetic energy of the car C =

The kinetic energy of the car D =

Given that work required = Force × Distance, and the distance, is constant, we have;

The force required is directly proportional to the energy kinetic energy of the car that is to be stopped

Therefore, we have;

B = 1, C = 2, A = 3, and D = 4

The work needed to stop the car, W = The strength of the applied force, F × The given constant distance to stop, d.

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Part A;

he mass of the object, m = 2 kg

The initial speed of the object, u = 3 m/s east

The final speed of the object, v = 7 m/s west

The initial kinetic energy of the object = 1/2 × m × u² = 1/2 × 2 × 3² = 9 Joules

The final kinetic energy of the object = 1/2 × m × v² = 1/2 × 2 × 7² = 49 Joules

Based on the change in the momentum produced by the force which changes the direction  of the object, we add the two energy quantities to get the total change in energy as follows;

The change in kinetic energy = 9 J + 49 J = 58 J

The statement is wrong because the change in momentum brought about by the force should be included when finding the the total change in kinetic energy of the object during the 5 seconds period

Part B;

The kinetic energy, K. E. = 1/2 × m × v²

The kinetic energy of the car A = 1/2 × 1000 × 6² = 18,000 J

The kinetic energy of the car B = 1/2 × 1600 × 8² = 51,200 J

The kinetic energy of the car C = 1/2 × 1200 × 8² = 38,400 J

The kinetic energy of the car D = 1/2 × 1600 × 4² = 12,800 J

Given that work required = Force × Distance, and the distance, is constant, we have;

The force required is directly proportional to the energy kinetic energy of the car that is to be stopped

Therefore, we have;

B = 1, C = 2, A = 3, and D = 4

The work needed to stop the car, W = The strength of the applied force, F × The given constant distance to stop, d

∴ W ∝ F.

Explanation:

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