Question

Runner whose mass is 50 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? average force = 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? displacement = m
(c) therefore, how much work is done on the extended system (the runner) by the force you calculated in part (b)? work = j
(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.) work = j
(e) the kinetic energy of the runner increases; what kind of energy decreases? (in this short run, there has not been a significant temperature change in the runner.) translational kinetic energy rotational kinetic energy thermal energy gravitational energy chemical energy correct: your answer is correct.
(f) what is the change of the energy you identified in part (e)? pay attention to signs. energy change = j

Answer 1

The average force exerted by the runner on the ground is 150 N.

Step-by-step explanation:

To calculate the average force exerted by the runner on the ground, we can use the equation:

Force = (Change in momentum) / (Time taken)

First, we need to calculate the change in momentum:

Change in momentum = (final momentum) - (initial momentum)

Given that the mass of the runner is 50 kg, the initial velocity is 0 m/s, and the final velocity is 6 m/s, we can calculate the initial momentum and final momentum:

Initial momentum = mass * initial velocity = 50 kg * 0 m/s = 0 kg·m/s

Final momentum = mass * final velocity = 50 kg * 6 m/s = 300 kg·m/s

Substituting these values into the equation, we have:

Change in momentum = (300 kg·m/s) - (0 kg·m/s) = 300 kg·m/s

Next, we need to calculate the time taken, which is given as 2 seconds:

Time taken = 2 seconds

Finally, substituting the values into the equation, we can calculate the average force:

Force = (300 kg·m/s) / (2 seconds) = 150 N