A man in a circus shows jumps from a of 10m and is caught by the safety net which sags 2m due to his weight.calculate the average force exerted by the net on the man to stop his fall if the mass of the man is 60kg
force*distancesagging=mass*g*30m
3000N
300N
To calculate the average force exerted by the net on the man, we need to 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.
First, let's calculate the acceleration of the man due to gravity. We can use the formula for acceleration:
acceleration = change in velocity / time taken.
Since the man starts from rest at the top of the jump and comes to a stop at the bottom, the change in velocity is equal to the final velocity (0 m/s) minus the initial velocity. The initial velocity can be calculated using the equation:
initial velocity = square root(2 * gravity_constant * height),
where gravity_constant is approximately 9.8 m/s² (acceleration due to gravity) and height is the total distance of the fall (10 m + 2 m = 12 m). Therefore:
initial velocity = square root(2 * 9.8 * 12) ≈ 16.97 m/s.
Since the final velocity is zero, the change in velocity is -16.97 m/s.
Now, we can calculate the acceleration:
acceleration = change in velocity / time taken.
The time taken can be calculated using the equation:
time taken = square root(2 * height / gravity_constant),
where height is the total distance of the fall (10 m + 2 m = 12 m). Therefore:
time taken = square root(2 * 12 / 9.8) ≈ 1.79 s.
Now that we have the acceleration, we can calculate the average force exerted by the net on the man using the formula:
force = mass * acceleration.
Given that the mass of the man is 60 kg, we have:
force = 60 kg * acceleration.
Plugging in the value for acceleration, we get:
force = 60 kg * (change in velocity / time taken).
force = 60 kg * (-16.97 m/s) / 1.79 s.
Simplifying, we find:
force ≈ -569.83 N.
Note that the negative sign indicates that the force is directed upward, opposing the downward motion of the man during the fall.