What is the magnitude of the acceleration of two falling sky divers (mass 149 kg including parachute) when the upward force of air resistance is equal to one fourth of their weight?
(in m/s^2)
After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?
(in N)
Madison, Ashley, cait, Tanner, et al. You need to show some work on your part. This is not a homework dump site.
I had a problem with this too, though.
For the first part I did basically g/4 ( M x g/4 = M x a) which should have been 2.45m/s^2 but apparently that's wrong, and I can't figure out why.
To find the magnitude of the acceleration of the skydivers when the upward force of air resistance is equal to one-fourth of their weight, we can start by understanding the forces acting on the skydivers.
When an object is falling through the air, it experiences two main forces: the force of gravity pulling it down and the opposite force of air resistance pushing it up. These forces can be represented by the equations:
Weight = mass * acceleration due to gravity (W = m * g)
Air resistance = coefficient * speed^2 (R = k * v^2)
In this case, we are given that the upward force of air resistance is equal to one-fourth of the skydivers' weight. So we can set up the equation:
1/4 * Weight = Air resistance
Substituting the equations above, we get:
1/4 * (m * g) = k * v^2
Since we're looking to find the magnitude of the acceleration, we can use Newton's second law:
Force = mass * acceleration
In this case, the resultant force acting on the skydivers is the difference between the weight and the air resistance:
Resultant force = Weight - Air resistance
Now, let's solve for the magnitude of the acceleration:
1) Substitute the expression for the weight and air resistance into the resultant force equation:
Resultant force = m * g - k * v^2
2) Equate the resultant force to mass times acceleration:
m * a = m * g - k * v^2
3) Cancel out the mass on both sides:
a = g - (k * v^2) / m
Now you can calculate the magnitude of the acceleration using the given values for the mass (m = 149 kg) and the acceleration due to gravity (g = 9.8 m/s^2), as well as the coefficient of air resistance (k).
To calculate the force of air resistance after the parachute is open, we need to consider that the skydivers descend leisurely to the ground at a constant speed. This means that the force of air resistance is equal in magnitude but opposite in direction to the force of gravity.
So, in this case, the force of air resistance on the skydivers and their parachute is equal to their weight. Since we already calculated the weight as mass times the acceleration due to gravity (W = m * g), we can simply use that value to find the force of air resistance.
Remember to use the given mass including the parachute, and the value of the acceleration due to gravity.