The Rusty Atwoods Machine: Two masses are suspended from a pulley attached to th

Question

The Rusty Atwoods Machine: Two masses are suspended from a pulley attached to the ceiling. One mass, m2 is heavier than the other, m1, i.e., m2 >m. Mass m2 is released a distance h from the floor, and falls while m is lifted up. Ignore the size of the blocks in all cases 101: Mechanics Semester: Fall 2017 (a) First, assume there is no friction in the pulley. Using conservation of energy write an expression for the speed of mass m2 when it is a distance d above the (2 points) (1 point) Now, assume that there is a constant force of friction caused by rust on the pulleys axle. The rusty axle exerts a constant force F in opposition to the direction of floor (b) In this frictionless case, at what speed does m2 hit the floor? motion of the rope as the wheel turns (c) Incorporating this dissipative force, write a new expression for the speed of mas (3 points) (2 points) m2 when it is a distance d above the floor (d) In this case, at what speed does m2 hit the floor?

Explanation / Answer

a)

using conservation of energy

initial Potential energy = final potential energy + final Kinetic energy

m2 gh = m1 g(h - d) + m2 g d + (0.5) (m1 + m2) v2

(m2 - m1) gh + (m1 - m2) gd = (0.5) (m1 + m2) v2

v = sqrt(2 (m2 - m1) g (h - d)/(m1 + m2))

b)

using conservation of energy

initial Potential energy = final potential energy + final Kinetic energy

m2 gh = m1 g(h) + (0.5) (m1 + m2) v2

(m2 - m1) gh = (0.5) (m1 + m2) v2

v = sqrt(2 (m2 - m1) g h)/(m1 + m2))

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