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, which states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration:
Force (F) = Mass (m) * Acceleration (a)
In this case, the mass of the man (m) is given as 60 kg, and the acceleration (a) is given as 10 m/s^2 (due to gravity). We need to find the force exerted by the net (F).
First, let's calculate the velocity (v) of the man just before he hits the net. We can use the equation of motion:
v^2 = u^2 + 2as
where:
v = final velocity (0 m/s, as the man stops)
u = initial velocity (unknown)
a = acceleration (due to gravity, 10 m/s^2)
s = distance traveled (10 m)
Since the man is falling from rest (u = 0) and comes to a stop (v = 0), we can rearrange the equation as follows:
0 = 0^2 + 2 * 10 * s
Simplifying:
0 = 20s
This gives us s = 0, which means the man has fallen a distance of zero when he hits the net.
Now, let's consider the force required to stop the man's fall, which is equal to his weight. Weight is calculated as the mass multiplied by the acceleration due to gravity (g):
Weight (W) = mass (m) * acceleration due to gravity (g)
In this case, g is approximately 9.8 m/s^2. So the weight (W) of the man is:
W = 60 kg * 9.8 m/s^2 = 588 N
Since the net sags 2m due to the impact, the distance traveled by the man after the initial impact is 2m.
To calculate the average force (F) exerted by the net on the man, we can use the formula:
F = Change in Momentum / Time
Change in momentum is equal to the weight (W) of the man multiplied by the distance traveled (2m):
Change in momentum = W * 2 = 588 N * 2 m = 1176 N * m
Now, we need to calculate the time (t) it takes for the man to stop. We can use the equation of motion:
v = u + at
where:
v = final velocity (0 m/s, as the man stops)
u = initial velocity (unknown)
a = acceleration (due to gravity, 10 m/s^2)
t = time taken (unknown)
Since u = 0 and v = 0, we can rearrange the equation as follows:
0 = 0 + 10t
Simplifying:
0 = 10t
This gives us t = 0 seconds, which means the man stops instantaneously.
Therefore, the average force (F) exerted by the net on the man to stop his fall is:
F = Change in Momentum / Time
= 1176 N * m / 0 s
= Infinity
The average force exerted by the net on the man is infinite, as the net prevents the man's fall without any time interval.