A Rock of mass 32kg 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 256n.What is the magnitude of the acceleration of the rock. answer in m/s2
To find the magnitude of the acceleration of the rock, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
F_net = m * a
In this case, since the rock is falling straight down, the force of gravity (weight) will act downwards, and the force of air resistance will act upwards. Since these forces are in opposite directions, we need to subtract the magnitude of the air resistance from the weight to find the net force:
F_net = weight - air resistance
The weight of an object can be calculated using the formula:
weight = mass * gravitational acceleration
In this case, the mass of the rock is given as 32 kg, and the gravitational acceleration on Earth is approximately 9.8 m/s². Substituting these values in:
weight = 32 kg * 9.8 m/s² = 313.6 N
Now we can calculate the net force:
F_net = 313.6 N - 256 N = 57.6 N
Finally, using Newton's second law, we can find the acceleration:
F_net = m * a
a = F_net / m = 57.6 N / 32 kg ≈ 1.8 m/s²
Therefore, the magnitude of the acceleration of the rock is approximately 1.8 m/s².