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I just recently got my midterm back and I felt this was graded wrong...

I dont have a picture..but just picture a ramp inclined to [tex] \phi=30[/tex] One mass is sitting on the incline...And the other is dangling from a rope which runs over a pulley

Two masses [tex]m_1[/tex] & [tex]m_2[/tex] both have a mass of 2Kg. If [tex]m_1[/tex] slide up the ramp at a constant velocity, what is the kinetic frictional force on [tex]m_1[/tex]? Assume that the masses of the rope and pulley are negligible, and that the pulley is frictionless.

How I did it...

[tex]m_1 x/ T-f_k = m_1a[/tex] (Eq1)

[tex] y/ N-mgsin \phi=0[/tex]

[tex]m_2 x/ T-mgsin \phi=m_2a[/tex]

[tex] y/ T=mgsin \phi[/tex] (Eq2)

-------------------------------------------------

isolate T in Eq1

[tex]T-f_k=m_1a[/tex] Since a=0

[tex]T=f_k[/tex]

Sub Eq2 into Eq1

[tex]mgsin \phi=f_k[/tex]

[tex]2Kg(9.8m/s)sin \phi=f_k[/tex]

[tex]f_k=9.8N[/tex]

Although i got the right answer he says that it needs to be expressed like this

[tex]T-f_k-mgsin \phi=0[/tex]

[tex]f_k=T-mgsin \phi[/tex] T=mg

[tex]f_k=mg-mgsin \phi = 9.8N[/tex]

Why is my way wrong?

I dont have a picture..but just picture a ramp inclined to [tex] \phi=30[/tex] One mass is sitting on the incline...And the other is dangling from a rope which runs over a pulley

Two masses [tex]m_1[/tex] & [tex]m_2[/tex] both have a mass of 2Kg. If [tex]m_1[/tex] slide up the ramp at a constant velocity, what is the kinetic frictional force on [tex]m_1[/tex]? Assume that the masses of the rope and pulley are negligible, and that the pulley is frictionless.

How I did it...

[tex]m_1 x/ T-f_k = m_1a[/tex] (Eq1)

[tex] y/ N-mgsin \phi=0[/tex]

[tex]m_2 x/ T-mgsin \phi=m_2a[/tex]

[tex] y/ T=mgsin \phi[/tex] (Eq2)

-------------------------------------------------

isolate T in Eq1

[tex]T-f_k=m_1a[/tex] Since a=0

[tex]T=f_k[/tex]

Sub Eq2 into Eq1

[tex]mgsin \phi=f_k[/tex]

[tex]2Kg(9.8m/s)sin \phi=f_k[/tex]

[tex]f_k=9.8N[/tex]

Although i got the right answer he says that it needs to be expressed like this

[tex]T-f_k-mgsin \phi=0[/tex]

[tex]f_k=T-mgsin \phi[/tex] T=mg

[tex]f_k=mg-mgsin \phi = 9.8N[/tex]

Why is my way wrong?

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