a men in circus shows jump from a height of 10m &caught by net spread below the net sag 2m due to its impact.find avgforce exerted by net on man to stop hiss fall .takeamassofman60kg and acceleration10m/s2
To find the average force exerted by the net on the man to stop his fall, we can use Newton's second law of motion:
Force = mass * acceleration
In this case, the mass of the man is given as 60 kg, and the acceleration due to gravity is approximately 10 m/s^2.
First, let's calculate the initial velocity of the man just before he hits the net. We can use the kinematic equation:
v^2 = u^2 + 2as
where v is the final velocity (which is 0 m/s as the man comes to a stop), u is the initial velocity (which we need to calculate), a is the acceleration due to gravity (-10 m/s^2), and s is the total distance covered (10 m + 2 m = 12 m).
Rearranging the equation, we have:
u^2 = v^2 - 2as
u^2 = 0 - 2 * (-10) * 12
u^2 = 240
u = √240
u ≈ 15.49 m/s (rounded to two decimal places)
Now, let's find the time it takes for the man to fall through a height of 10 m. We can use the equation:
s = ut + (1/2)at^2
where s is the distance (10 m), u is the initial velocity (15.49 m/s), a is the acceleration due to gravity (-10 m/s^2), and t is the time.
Substituting the known values into the equation, we have:
10 = (15.49)t + (1/2)(-10)t^2
Rearranging the equation, we get a quadratic equation:
-5t^2 + 15.49t - 10 = 0
To solve this quadratic equation, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = -5, b = 15.49, and c = -10. Plugging the values into the formula, we get:
t = (-15.49 ± √(15.49^2 - 4(-5)(-10))) / (2(-5))
t = (-15.49 ± √(239.0401)) / (-10)
t ≈ (-15.49 ± 15.46) / (-10)
We have two possible values for t:
t1 ≈ (-15.49 + 15.46) / (-10) ≈ 0.03 s (rounded to two decimal places)
t2 ≈ (-15.49 - 15.46) / (-10) ≈ -0.001 s (rounded to three decimal places)
Since time cannot be negative, t2 can be disregarded. Therefore, the time it takes for the man to fall through a height of 10 m is approximately 0.03 s.
Now, we can calculate the average force exerted by the net on the man using Newton's second law of motion:
Force = mass * acceleration
Force = 60 kg * 10 m/s^2
Force = 600 N
Therefore, the average force exerted by the net on the man to stop his fall is 600 Newtons.