A 70 kg man just before contact with the ground has a speed of 5 m/s In a stiff-legged landing he comes to a halt in 7ms (miliseconds). Keeping in mind that the average net force acting on the man includes both the force of the ground on the man and the gravity force, find the force of the ground on the man.
To find the force of the ground on the man, we can use the equation:
Force = Mass * Acceleration
The mass of the man is given as 70 kg, and we need to find the acceleration.
We can use the equation of motion:
v = u + at
where,
v = final velocity (0 m/s, as the man comes to a halt)
u = initial velocity (5 m/s)
a = acceleration
t = time (7 ms = 0.007 s)
Rearranging the equation, we have:
a = (v - u) / t
Substituting the given values, we have:
a = (0 - 5) / 0.007
= -5 / 0.007
= -714.3 m/s^2
Since the man came to a halt, the acceleration is negative, indicating it is in the opposite direction to the initial velocity.
Now we can find the force:
Force = Mass * Acceleration
Force = 70 kg * (-714.3 m/s^2)
= -50,000 N
The force of the ground on the man is -50,000 Newtons, with the negative sign indicating that it is acting in the opposite direction to the man's motion.
To find the force of the ground on the man, we need to analyze the change in velocity and apply Newton's second law of motion.
Newton's second law of motion states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. Mathematically, it can be expressed as:
F = m * a
In this case, the man comes to a halt in 7 milliseconds, which means his change in velocity, Δv, is equal to his initial velocity since his final velocity is zero:
Δv = 5 m/s
Now, we need to find the acceleration, a. The acceleration can be calculated using the formula:
a = Δv / Δt
where Δt is the time interval. In this case, Δt is given as 7 milliseconds, but it's more convenient to convert it to seconds before plugging it into the formula. Therefore, Δt = 7 milliseconds = 0.007 seconds.
Plugging the values into the formula, we get:
a = Δv / Δt = 5 m/s / 0.007 s
Solving this equation, we find:
a ≈ 714.29 m/s²
Now, we have the acceleration. To find the force of the ground on the man, we can use Newton's second law:
F = m * a
Plugging in the given mass of the man (70 kg) and the acceleration we calculated, we get:
F = 70 kg * 714.29 m/s²
Calculating this, we find:
F ≈ 50,000 N
Therefore, the force of the ground on the man is approximately 50,000 Newtons.