A block of mass m_1, on an incline with angle theta, is attached to another bloc

Question

A block of mass m_1, on an incline with angle theta, is attached to another block of mass m_2, on a flat surface, with a massless rope that passes over a frictionless ring. A large horizontal force, F, pulls mass m_2 to the right, as shown m the figure. The coefficient of kinetic friction, mu_k, between the blocks and surfaces is die same everywhere. a) Draw the free body diagrams (i.e. indicate all forces acting on each block) and write the corresponding Newton s Force equations-of-motion for that block. Clearly indicate your choice of axes on the free body diagrams. b) Solve for the acceleration of the system in terms of the horizontal force F_1, m_1, m_2, mu_k, theta, and g. c) Calculate the minimum horizontal force F needed to pull both blocks to the right at constant speed given the following values: m_1 = 10.0 kg, m_2 = 20.0 kg, mu_k = 0.200, theta = 25 degree and g = 9.8 m/s^2.

Explanation / Answer

for m1

Fnet = m1*a

T - uk*m1*g*costheta - m1*g*sintheta = m1*a .....(1)

for m2

Fnet = m2*a

F - T - uk*m2*g = m2*a..........(2)

solving 1 & 2

F - uk*m1*g*costheta - m1*g*sintheta - uk*m2*g = (m1+m2)*a

a = (F - uk*m1*g*costheta - m1*g*sintheta - uk*m2*g )/(m1+m2)

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(c)

at constant speed acceleration a = 0

(F - uk*m1*g*costheta - m1*g*sintheta - uk*m2*g ) = 0

F - (0.2*10*9.8*cos25) - (10*9.8*sin25) - (0.2*20*9.8) = 0

F = 98.4 N <<<<=======answer

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