What is the acceleration of two falling sky divers (mass 107.0 kg including parachute) when the upward force of air resistance is equal to one-fourth of their weight?
To find the acceleration of the two falling skydivers, we need to use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
Given that the upward force of air resistance is equal to one-fourth of their weight, we can calculate the magnitude of air resistance acting on each skydiver.
Step 1: Calculate the weight of each skydiver:
Weight = mass * acceleration due to gravity
Since the mass given includes the parachute, we need to subtract the mass of the parachute to find the mass of each skydiver.
Mass of skydiver = mass including parachute - mass of parachute
Step 2: Calculate the magnitude of air resistance for each skydiver:
Magnitude of air resistance = 1/4 * weight
Step 3: Calculate the net force on each skydiver:
Net force = Weight - Magnitude of air resistance
Step 4: Use Newton's second law to find the acceleration:
Acceleration = Net force / mass of skydiver
By following these steps, you can find the acceleration of the two falling skydivers.
To find the acceleration of the skydivers, we need to use Newton's second law of motion, which states that the force on an object is equal to its mass multiplied by its acceleration (F = m * a).
In this case, the upward force of air resistance is equal to one-fourth of the weight of the skydivers. The weight of an object is given by the equation W = m * g, where m is the mass and g is the acceleration due to gravity (which is approximately 9.8 m/s^2 on Earth).
So, the force of air resistance is equal to (1/4) * (mass * g). We can set this equal to the net force on the skydivers, which is also equal to m * a.
(1/4) * (mass * g) = mass * a
Next, we can rearrange the equation to solve for acceleration (a):
a = (1/4) * (g)
Plugging in the value of g (approximately 9.8 m/s^2):
a = (1/4) * 9.8
a = 2.45 m/s^2
Therefore, the acceleration of the two falling skydivers, when the upward force of air resistance is equal to one-fourth of their weight, is 2.45 m/s^2.