How Is Work Calculated in a Point-Particle System for a Sprinting Runner?

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A runner with a mass of 49 kg accelerates to 6 m/s in 2 seconds, resulting in an average horizontal force of 147 N exerted by the ground. The displacement of this force on the runner's shoes is 0 m, leading to zero work done on the real system. However, the work done on the point-particle system requires applying fundamental principles. The discussion highlights the calculations for force and work, with the user successfully resolving the final part of the problem. The thread emphasizes understanding the relationship between force, displacement, and work in a point-particle context.
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Homework Statement



A runner whose mass is 49 kg accelerates from a stop to a speed of 6 m/s in 2 seconds. (A good sprinter can run 100 meters in about 10 seconds, with an average speed of 10 m/s.)

(a) What is the average horizontal component of the force that the ground exerts on the runner's shoes? I got the answer for this which is 147 N.

(b) How much displacement is there of the force that acts on the sole of the runner's shoes, assuming that there is no slipping? I got the answer for this one too = 0 m

(c) Therefore, how much work is done on the real system (the runner) by the force you calculated in part (b)? I also got 0 for this one since its F x d

(d) How much work is done on the point-particle system by this force? (Hint: use a fundamental principle, as applied to the point-particle system.)


The Attempt at a Solution



I got a,b,c am just having problems with part d. Thanks a lot
 
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lebprince said:

Homework Statement



A runner whose mass is 49 kg accelerates from a stop to a speed of 6 m/s in 2 seconds. (A good sprinter can run 100 meters in about 10 seconds, with an average speed of 10 m/s.)

(a) What is the average horizontal component of the force that the ground exerts on the runner's shoes? I got the answer for this which is 147 N.

(b) How much displacement is there of the force that acts on the sole of the runner's shoes, assuming that there is no slipping? I got the answer for this one too = 0 m

(c) Therefore, how much work is done on the real system (the runner) by the force you calculated in part (b)? I also got 0 for this one since its F x d

(d) How much work is done on the point-particle system by this force? (Hint: use a fundamental principle, as applied to the point-particle system.)


The Attempt at a Solution



I got a,b,c am just having problems with part d. Thanks a lot

figured it out thanks
 

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