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Book1 has a mass of 8.60 kg. Book 2 sits on top of book 1 has a mass of 1.30 kg. ?
They are linked by a rope which passes over a pulley at the top of the incline The plane is at an angle of 38.0° with respect to the horizontal. What is the amount of force with direction to prevent the sliding of the books if the surfaces are frictionless?
1 Answer
- AshLv 71 month agoFavorite Answer
Mass of Book1, m₁ = 8.60 kg
Mass of Book2, m₂ = 1.30 kg
angle of incline, θ = 38.0°
Let's consider that the Book1 starts to slide downward along the incline
Force on Book1 is....
weight component downward along the incline, W₁ = m₁gsinθ
Force on Book2 is....
weight component downward along the incline, W₂ = m₂gsinθ
Let T₁ = tension on the rope attached to Book1
and T₂ = tension on the rope attached to Book2
Net force, F = T₁ - T₂
F = W₁ - W₂
F = m₁gsinθ - m₂gsinθ
F = (m₁ - m₂)gsinθ
F = (8.60 - 1.30)(9.81)sin38.0°
F = 44.1 N downward along the incline
So we have to apply an opposite force of 44.1 N upward along the incline, to the Book1 to stop the books from sliding