A steel block rests on a wooden plank 8m long.the coefficient of friction between steel and wood is 0.3 to what height must one end of the plank be lifted to make the block just begin to slide down the plank

Answer 1

To determine the height at which the block would begin to slide down the plank, we can use the following equation:

Frictional force = Force due to gravity down the plank

The frictional force is given by:

Frictional force = coefficient of friction x Normal force
Frictional force = 0.3 x weight of the block

The weight of the block is given by:

Weight = mass x gravity
Weight = density x volume x gravity
Weight = density x (length of plank x width of plank x height of plank) x gravity

Since the block is a steel block, we can assume the density of steel to be 7850 kg/m^3.

Now, we can equate the frictional force to the force due to gravity down the plank:

0.3 x weight of block = mass x gravity x sin(θ)

where θ is the angle of elevation at which the plank is lifted.

Now, we need to find the value of θ at which the block just begins to slide down the plank. This is when the frictional force is equal to the force due to gravity down the plane:

0.3 x (7850 x 8 x width x height x 9.81) = 7850 x 9.81 x sin(θ)

Solving for θ:

0.3 x 62800 x width x height = 78500 x sin(θ)
18840 x width x height = 7850 x sin(θ)
2.4 x width x height = sin(θ)

Therefore, the height at which one end of the plank must be lifted to make the block just begin to slide down the plank is sin^(-1)(2.4 x width).