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
Max. Height =10m
Mass of man= 60kg
Accelerating during freefall=10m/s2
initial velocity on max. height =0
Final velocity = v2-u2=2gh
=14.15 m/s
To calculate 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
Given:
Mass of the man (m) = 60 kg
Acceleration (a) = 10 m/s^2
We need to determine the force exerted by the net on the man, but first, we need to find the time it takes for the man to fall from the height of 10m and come to a stop.
Using the equation of motion:
Distance (d) = Initial Velocity (v0) × Time (t) + 0.5 × Acceleration (a) × Time^2
Here,
Initial Velocity (v0) = 0 (as the man is falling from rest)
Substituting the values,
10 m = 0 × t + 0.5 × 10 m/s^2 × t^2
Simplifying the equation:
10 m = 5 m/s^2 × t^2
Dividing both sides by 5 m/s^2:
2 m = t^2
Taking the square root of both sides:
t = √(2) ≈ 1.41 seconds
Now that we have the time taken for the man to fall and stop, we can calculate the average force exerted by the net 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 approximately 600 Newtons.
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 force (F) is equal to mass (m) multiplied by acceleration (a):
F = m * a
Given:
Mass of the man (m) = 60 kg
Acceleration (a) = 10 m/s²
Step 1: Calculate the weight of the man using the formula:
Weight = mass * acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s². So,
Weight = 60 kg * 9.8 m/s² = 588 N
Step 2:
When the man falls, the net sags by 2 m. This means that the net stretches by 2 m due to the impact.
Step 3:
To stop the fall completely, the average force exerted by the net on the man must be equal to the weight of the man. So, we need to find the force required to stretch the net by 2 m.
The force required to stretch a spring or a net can be calculated using Hooke's law, which states that force (F) is equal to the spring constant (k) multiplied by the displacement (x):
F = k * x
However, we don't have the spring constant for the net. Hence, we'll use a different approach.
We can analyze the fall of the man from a height of 10 m. At the point where the man is caught by the net, the net absorbs all the potential energy the man had due to his position at the top. This energy is equal to the work done by the net.
Step 4:
Calculate the potential energy of the man at the top using the formula:
Potential energy = mass * gravity * height
Potential energy = 60 kg * 9.8 m/s² * 10 m = 5880 Joules
Step 5:
Since the net sag is 2 m, the man's fall is reduced by 2 m. So, the net does work equal to the potential energy minus the potential energy at the point of stopping.
Work done by the net = Potential energy - (mass * gravity * sag)
Work done by the net = 5880 J - (60 kg * 9.8 m/s² * 2 m) = 5880 J - 1176 J = 4704 J
Step 6:
The average force exerted by the net on the man can be calculated using the formula:
Average force = Work done / Distance
In this case, the distance is equal to the sag, which is 2 m.
Average force = 4704 J / 2 m = 2352 N
Therefore, the average force exerted by the net on the man to stop his fall is 2352 Newtons.