To determine the acceleration of the block down the inclined slope, we need to consider the forces acting on the block. The main forces involved are the gravitational force (weight) and the component of the gravitational force parallel to the slope.
The weight of the block can be calculated using the formula: weight = mass * gravity, where gravity is approximately 9.8 m/s^2 on Earth. Therefore, the weight of the block is:
weight = 40 kg * 9.8 m/s^2 = 392 N
Since the slope is inclined at 45°, the component of the weight acting parallel to the slope can be found using trigonometry. The parallel component is given by:
parallel component = weight * sin(45°) = 392 N * sin(45°) ≈ 277.3 N
The acceleration of the block down the slope is determined by this parallel component. We can use Newton's second law of motion, which states that the net force on an object is equal to the product of its mass and acceleration (F = ma). In this case, the net force is the parallel component of the weight, and the mass is 40 kg. Therefore:
277.3 N = 40 kg * acceleration
Solving for acceleration:
acceleration = 277.3 N / 40 kg ≈ 6.93 m/s^2
Therefore, the acceleration of the block down the slope is approximately 6.93 m/s^2.