A concrete block of mass 25kg is placed on a wooden plank inclined at an angle of 32° to the horizontal.calculate the force parallel to the inclined plane that will keep the block at rest of the coefficient of friction between the block and the plank is 0.45
25 kg * g * cos(32º) * .45 = ? Newtons
use 9.8 m/s^2 for g
To calculate the force parallel to the inclined plane that will keep the block at rest, we need to determine the forces acting on the block.
1. Resolve the gravitational force:
The weight of the block can be resolved into two components: one perpendicular to the inclined plane and one parallel to the inclined plane.
Weight perpendicular to the inclined plane = m * g * cos(θ)
Weight parallel to the inclined plane = m * g * sin(θ), where θ is the angle of inclination (32°) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Weight perpendicular to the inclined plane = 25 kg * 9.8 m/s^2 * cos(32°) = 212.16 N
Weight parallel to the inclined plane = 25 kg * 9.8 m/s^2 * sin(32°) = 133.47 N
2. Determine the frictional force:
The frictional force can be calculated using the coefficient of friction (μ) and the weight perpendicular to the inclined plane.
Frictional force = μ * (Weight perpendicular to the inclined plane)
Frictional force = 0.45 * 212.16 N = 95.472 N
3. Calculate the force parallel to the inclined plane:
Since the block is at rest, the force parallel to the inclined plane must be equal to the frictional force to prevent the block from sliding down.
Force parallel to the inclined plane = Frictional force = 95.472 N.
Therefore, the force parallel to the inclined plane required to keep the block at rest is approximately 95.472 N.
To calculate the force parallel to the inclined plane that will keep the block at rest, we need to consider the forces acting on the block.
Let's break down the forces acting on the block along the inclined plane:
1. The weight of the block (downward force): The weight of the block can be calculated using the formula: weight = mass × acceleration due to gravity. In this case, weight = 25 kg × 9.8 m/s².
2. The normal force (perpendicular to the inclined plane): The normal force can be calculated using the formula: normal force = weight × cos(θ), where θ is the angle of inclination (32° in this case).
3. The frictional force (parallel to the inclined plane): The frictional force can be calculated using the formula: frictional force = coefficient of friction × normal force.
4. The force parallel to the inclined plane (needed to keep the block at rest): This force counteracts the component of the weight that is parallel to the inclined plane and is equal to the frictional force.
Let's calculate the forces:
Weight = 25 kg × 9.8 m/s² = 245 N
Normal force = 245 N × cos(32°) ≈ 208.19 N
Frictional force = 0.45 × 208.19 N ≈ 93.68 N
Therefore, the force parallel to the inclined plane that will keep the block at rest is approximately 93.68 N.