At a given instant in time, a 4.2-kg rock is observed to be falling with an acceleration of 8.4 m/s2. To two decimal places, what is the magnitude of the force of air resistance acting upon the rock at this instant?
To find the magnitude of the force of air resistance acting upon the rock, we can use Newton's second law of motion,
Fnet = ma
Where Fnet is the net force acting on the object, m is the mass of the object, and a is the acceleration of the object.
In this case, the net force acting on the rock is the sum of the force due to gravity and the force of air resistance.
Fnet = Fgravity + Fair
The force of gravity can be calculated using the equation,
Fgravity = mg
where g is the acceleration due to gravity (approximately 9.8 m/s²).
Given information:
Mass of the rock (m) = 4.2 kg
Acceleration of the rock (a) = 8.4 m/s²
Acceleration due to gravity (g) ≈ 9.8 m/s²
First, calculate the force of gravity:
Fgravity = mg = (4.2 kg) * (9.8 m/s²)
Next, calculate the net force acting on the rock using Newton's second law:
Fnet = ma = (4.2 kg) * (8.4 m/s²)
Finally, calculate the force of air resistance by subtracting the force of gravity from the net force:
Fair = Fnet - Fgravity
Now we can substitute the given values and calculate the magnitude of the force of air resistance.
To determine the magnitude of the force of air resistance acting on the rock, we need to use Newton's second law of motion:
F = m * a
Where:
F is the force acting on the object,
m is the mass of the object, and
a is the acceleration of the object.
In this case, the acceleration is given as 8.4 m/s^2, and the mass of the rock is 4.2 kg.
So, we can substitute these values into the equation to find the force of air resistance:
F = (4.2 kg) * (8.4 m/s^2)
F = 35.28 N
Therefore, the magnitude of the force of air resistance acting upon the rock at this instant is 35.28 N.