A steel block rests on a wooden plank, 6m long. At what height must the one end of the plank be lifted above the other end to allow the steel block to just start sliding down the plank if the coefficient of friction between and wood is 0,3?
To find the height at which the steel block will just start sliding down the plank, we need to consider the forces acting on the block.
The force causing the block to slide down the plank is the component of the weight of the block acting parallel to the plank. This force can be calculated as:
F = m * g * sin(theta)
Where:
F = Force causing the block to slide
m = Mass of the steel block
g = Acceleration due to gravity (9.81 m/s^2)
theta = Angle of the plank with the horizontal
The force of friction acting on the block can be calculated as:
f = coefficient of friction * N
Where:
f = Force of friction
N = Normal force acting on the block (equal to the component of the weight of the block perpendicular to the plank)
Since the block is just about to start sliding, the force causing the block to slide is equal to the force of friction. Therefore:
m * g * sin(theta) = coefficient of friction * N
Since N = m * g * cos(theta), we can substitute this into the equation to get:
m * g * sin(theta) = coefficient of friction * m * g * cos(theta)
Dividing both sides by m * g, we get:
sin(theta) = coefficient of friction * cos(theta)
Given that the coefficient of friction is 0.3, we can solve for the angle theta:
sin(theta) = 0.3 * cos(theta)
tan(theta) = 0.3
theta = arctan(0.3) = 16.7 degrees
Now that we know the angle theta, we can calculate the height at which one end of the plank must be lifted above the other end:
Height = 6m * sin(theta) = 6m * sin(16.7) = 1.67m
Therefore, the one end of the plank must be lifted 1.67 meters above the other end for the steel block to just start sliding down.