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.
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To calculate the average net force, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of the object's mass and its acceleration.
First, we need to find the acceleration. We can use the formula for acceleration:
acceleration = (final velocity - initial velocity) / time
Here, the initial velocity is given as 6.27 m/s, and the time is given as 2.06 ms. We need to convert the time to seconds:
time = 2.06 ms = 2.06 × 10^(-3) s
Using the formula, we can calculate the acceleration:
acceleration = (0 - 6.27) / 2.06 × 10^(-3) = -6.27 / 2.06 × 10^(-3) = -3043.69 m/s²
Since the man is coming to a halt, the final velocity is 0 m/s.
Now that we have the acceleration, we can find the average net force using Newton's second law:
net force = mass × acceleration
The mass of the man is given as 79.1 kg. Plugging in the values:
net force = 79.1 kg × (-3043.69 m/s²) = -240,405.779 N
Therefore, the average net force acting on the man during the landing is approximately -240,405.779 Newtons. The negative sign indicates that the force is acting in the opposite direction of motion.