Newton's Laws and Uniform Circular Motion Q2. Please answer and explain step by step and reasoning. Problem 2: A block with a mass of m = 1.5 kg rests on a wooden plank. Thecoefficient of static friction between the block and the plank is µ, = 0.86. One end ofthe board is attached to a hinge so that the other end can be lifted forming an angle, 0,with respect to the ground. Assume the x-axis is along the plank as shown in the figure.Part (a) Please use the interactive area below to draw the Free Body Diagram for this block, assuming it is in static equilibrium. If necessary, useFs for the force of static friction, and Fk for the force of kinetic friction.FBD :Force Labels:Fn, Fg, Fs, Fk, a, v45,0, 90, 135, 180, 225, 270, 315, 0Angle Labels:Part (b) Assuming the x-direction is along the plank as shown, find an expression for the magnitude of the force of gravity in the y-direction, Fgy,perpendicular to the plank in terms of given quantities and variables available in the palette.Expression :FgySelect from the variables below to write your expression. Note that all variables may not be required.acotan(u,), atan(µ), cos(a), cos(4), cos(0), sin(a), sin(4), sin(0), tan(0), a, ß, µ̟, Hg, 0, b, d, g, h, m, tPart (c) Write an expression for the magnitude of the maximum friction force along the surface, F,, in terms of given quantities and variablesavailable in the palette.Expression :F =Select from the variables below to write your expression. Note that all variables may not be required.acotan(u,), atan(µ̟), cos(a), cos(4), cos(0), sin(a), sin(4), sin(0), a, µk, µs, b, g, m, tPart (d) Assuming the static friction is maximized, write an expression, using only the given parameters and variables available in the palette, forthe sum of the forces along the plank, EFr.Expression :ΣFxSelect from the variables below to write your expression. Note that all variables may not be required.acotan(u,), atan(u), cos(a), cos(4), cos(0), sin(a), sin(4), sin(0), a, µk, µs, b, g, m, tPart (e) Write an expression for the maximum angle, 0m, that the board can make with respect to the horizontal before the block starts moving.(Write in terms of the given parameters and variables available in the palette.)Expression :Om =Select from the variables below to write your expression. Note that all variables may not be required.acotan(u,), atan(u.), cos(a), cos(4), cos(0), sin(a), sin(o), sin(0), tan(0), a, µ̟k, µs, 0, b, tPart (f) Solve numerically for the maximum angle, Om, in degrees.Numeric : A numeric value is expected and not an expression.Om

Answered: Problem 2: A block with a mass of m 1.5…

Physics for Scientists and Engineers, Technology Update (No access codes included)

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ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

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Chapter12: Static Equilibrium And Elasticity

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Newton's Laws and Uniform Circular Motion Q2. Please answer and explain step by step and reasoning.

Problem 2: A block with a mass of m = 1.5 kg rests on a wooden plank. The
coefficient of static friction between the block and the plank is µ, = 0.86. One end of
the board is attached to a hinge so that the other end can be lifted forming an angle, 0,
with respect to the ground. Assume the x-axis is along the plank as shown in the figure.
Part (a) Please use the interactive area below to draw the Free Body Diagram for this block, assuming it is in static equilibrium. If necessary, use
Fs for the force of static friction, and Fk for the force of kinetic friction.
FBD :
Force Labels:
Fn, Fg, Fs, Fk, a, v
45,0, 90, 135, 180, 225, 270, 315, 0
Angle Labels:
Part (b) Assuming the x-direction is along the plank as shown, find an expression for the magnitude of the force of gravity in the y-direction, Fgy,
perpendicular to the plank in terms of given quantities and variables available in the palette.
Expression :
Fgy
Select from the variables below to write your expression. Note that all variables may not be required.
acotan(u,), atan(µ), cos(a), cos(4), cos(0), sin(a), sin(4), sin(0), tan(0), a, ß, µ̟, Hg, 0, b, d, g, h, m, t
Part (c) Write an expression for the magnitude of the maximum friction force along the surface, F,, in terms of given quantities and variables
available in the palette.
Expression :
F =
Select from the variables below to write your expression. Note that all variables may not be required.
acotan(u,), atan(µ̟), cos(a), cos(4), cos(0), sin(a), sin(4), sin(0), a, µk, µs, b, g, m, t
Part (d) Assuming the static friction is maximized, write an expression, using only the given parameters and variables available in the palette, for
the sum of the forces along the plank, EFr.
Expression :
ΣFx
Select from the variables below to write your expression. Note that all variables may not be required.
acotan(u,), atan(u), cos(a), cos(4), cos(0), sin(a), sin(4), sin(0), a, µk, µs, b, g, m, t
Part (e) Write an expression for the maximum angle, 0m, that the board can make with respect to the horizontal before the block starts moving.
(Write in terms of the given parameters and variables available in the palette.)
Expression :
Om =
Select from the variables below to write your expression. Note that all variables may not be required.
acotan(u,), atan(u.), cos(a), cos(4), cos(0), sin(a), sin(o), sin(0), tan(0), a, µ̟k, µs, 0, b, t
Part (f) Solve numerically for the maximum angle, Om, in degrees.
Numeric : A numeric value is expected and not an expression.
Om

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Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.

Solution:-

1) The co-efficient of static friction between any object and surface of inclined plane(i.e. plank) , is given by

tanθ = μ_s

Here, μ_s = coefficient of static friction

θ = angle of the inclination

2) The force of gravity on an object of mass m , is given by

F_g = mg_e

Here, m = mass of object

g_e = gravitational acceleration of earth

This, acts always vertically downward.

3) The maximum value of force of friction, is given by

f_max = f_s = μ_sR

Here, μ_s= co-efficient of static friction

R = contact force on block by the surface of incline

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