A rock of mass 44 kg accidentally breaks loose from the edge of a cliff and falls straight down. The magnitude of the air resistance that opposes its downward motion is 258 N. What is the magnitude of the acceleration of the rock?
Fn = Fr - Fa,
Fn = 32*9.8 - 258 = 55.6 N.=Net force.
a = Fn/m = 55.6 / 32 = 1.74 m/s^2.
Correction: In each Eq, replace 32 with 44 and recalculate.
To find the magnitude of the acceleration of the rock, we need to determine the net force acting on it.
The net force is the difference between the gravitational force and the air resistance force.
The gravitational force acting on the rock can be calculated using the equation:
Force_gravity = mass * acceleration_due_to_gravity
where mass is the mass of the rock (44 kg) and acceleration_due_to_gravity is the acceleration due to gravity (9.8 m/s^2).
Force_gravity = 44 kg * 9.8 m/s^2 = 431.2 N
The net force acting on the rock is then given by:
Net_force = Force_gravity - Force_air_resistance
Net_force = 431.2 N - 258 N = 173.2 N
Finally, we can calculate the magnitude of the acceleration using Newton's second law:
Net_force = mass * acceleration
Therefore,
173.2 N = 44 kg * acceleration
Dividing both sides by 44 kg, we find:
acceleration = 173.2 N / 44 kg = 3.937 m/s^2
Hence, the magnitude of the acceleration of the rock is 3.937 m/s^2.
To find the magnitude of the acceleration of the rock, we need to consider the forces acting on it. There are two main forces at play: the force of gravity pulling the rock downward and the force of air resistance opposing its motion.
First, let's consider the force of gravity. The force of gravity can be calculated using the formula:
F_gravity = mass * acceleration_due_to_gravity
where mass is the mass of the rock and acceleration_due_to_gravity is the acceleration due to gravity, which is approximately 9.8 m/s² on Earth.
F_gravity = 44 kg * 9.8 m/s² = 431.2 N
Next, we can calculate the net force acting on the rock. Since air resistance opposes the motion, its direction is opposite to that of the gravitational force. The net force is the vector sum of the gravitational force and the force of air resistance.
Net force = F_gravity - F_air_resistance
F_air_resistance = 258 N (given)
Net force = 431.2 N - 258 N = 173.2 N
Finally, we can determine the acceleration of the rock using Newton's second law of motion:
Net force = mass * acceleration
Rearranging the equation, we have:
acceleration = Net force / mass
acceleration = 173.2 N / 44 kg ≈ 3.94 m/s²
Therefore, the magnitude of the acceleration of the rock is approximately 3.94 m/s².