When jumping straight down, you can be seriously injured if you land stiff-legged. One way to avoid injury is to bend your knees upon landing to reduce the force of the impact. A 79.1 kg man just before contact with the ground has a speed of 6.27 m/s. In a stiff-legged landing he comes to a halt in 2.06 ms. Calculate the average net force that acts on him during this time.
force = rate of change of momentum (only m a if m is constant :)
change of momentum = 79.1 (0 - -6.27)
change of time = 2.06*10^-3 s
so
force = + 6.27*79.1 / .00206 Newtons
To calculate the average net force, we can use the equation:
Net force = (change in momentum) / (time taken)
First, we need to calculate the change in momentum. The momentum of an object is given by the equation:
Momentum = mass × velocity
The initial momentum can be calculated as:
Initial momentum = mass × initial velocity
Final momentum = mass × final velocity
In this case, the initial velocity is 6.27 m/s and the final velocity is 0 m/s (since the person comes to a halt). The mass of the person is given as 79.1 kg.
Initial momentum = 79.1 kg × 6.27 m/s
Final momentum = 79.1 kg × 0 m/s
Next, we can calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
Now, we need to convert the time given in milliseconds to seconds:
Time taken = 2.06 ms = 2.06 × 10^(-3) s
Finally, we can substitute the values into the equation for average net force:
Average net force = (change in momentum) / (time taken)
Now, let's calculate the average net force:
Initial momentum = 79.1 kg × 6.27 m/s = 496.457 kg·m/s
Final momentum = 79.1 kg × 0 m/s = 0 kg·m/s
Change in momentum = Final momentum - Initial momentum = 0 - 496.457 kg·m/s = -496.457 kg·m/s
Time taken = 2.06 × 10^(-3) s
Average net force = (-496.457 kg·m/s) / (2.06 × 10^(-3) s)
Therefore, the average net force that acts on the man during this time is approximately -240908.3 N (rounded to one decimal place). The negative sign indicates that the force is directed upwards, opposing the motion of the man.