QUIZ 1 AND 2, PROBLEM 3

Question

A block of mass M is pulled with a rope that exerts a force of a magnitude F, causing it to slide over horizontal ground with kinetic coefficient of friction μ (use "mu" when you input your answer). The force is applied at angle θ (use "theta" when you input your answer) above the horizontal shown below.

1) Resolve F⃗ into components using the coordinate system shown.

Fx,Fy=
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μ⋅N
,

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m⋅g
2) Find the sum of the force components in the y-direction acting on the mass (in terms of N,M,g,F, where N is the magnitude of the normal force exerted by the surface on the box). Do not evaluate your expression - that is, do not get a number. Give a formula instead.

∑Fy=
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3) Find the normal force of the ground acting on the mass.

N=
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m⋅g−F⋅sin(θ)
4) Find the net force in the x-direction acting on the mass (in terms of mu, F, M, g, theta):

∑Fx=
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F⋅cos(θ)−μ⋅(F⋅sin(θ)+N−M⋅g)
5) Find the acceleration of the mass in the x-direction (in terms of mu, F, M, g, theta).

a=
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F⋅cos(θ)−μ⋅(F⋅sin(θ)+N−M⋅g)M
6) The block has a normal force N, a friction force Ff, a gravitational force W, and F acting on it. Which of these relationships about the magnitudes of these forces is true when F is angled as shown and is just strong enough to keep the block moving at a constant speed along the ground?

F=Ff and N=W
F=Ff and N>W

F>Ff and N<W

F>Ff and N=W

F>Ff and N>W

F<Ff and N=W

none of the above