Question

Using energy considerations, calculate the average force (in N) a 70.0 kg sprinter exerts backward on the track to accelerate from 2.00 to 8.00 m/s in a distance of 25.0 m, if he encounters a headwind that exerts an average force of 30.0 N against him.

Answer 1

The average force a 70.0 kg sprinter exerts backward on the track is 84 N.

What is law of conservation of energy?

The law of conservation of energy states that energy can neither be created nor destroyed but can be converted from one form to another.

E = Fd

where;

• F is the applied force
• d is the displacement of the object

The average force exerted by the sprinter is calculated as follows;

F = ma

where;

• a is the acceleration of the sprinter
• m is mass of the sprinter

The acceleration of the sprinter is calculated as follows;

v² = u² + 2as

where;

• v is the final velocity
• u is the initial velocity
• s is the distance

(8)² = (2)² + (2x25)a

64 = 4 + 50a

60 = 50a

a = 60/50

a = 1.2 m/s²

Average force exerted by the sprinter;

F = ma

F = 70 kg x 1.2 m/s²

F = 84 N

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