An 8.0 kg mass, M, and a 2 kg mass m are suspended vertically from the top of a

Question

An 8.0 kg mass, M, and a 2 kg mass m are suspended vertically from the top of a massless, frictionless pulley using massless rope as shown in the diagram. Assume the system is initially at rest and at t = 0 mass M is released.

a) (4 points) Draw a free body diagram for each block that clearly indicates all the forces acting on each block. (Also put in a coordinate system with each block) mM

b) (4 points) Use Newton?s second law of the m motion of mass M to write an equation for M. _________________________________

(c) (4 points) Repeat part b for the motion of mass m. __________________________________

(d) (4 points) Solve for the magnitude of the acceleration of each block _________________________________

(e) (4 points) If M drops 1.5 meters how much work is done by gravity on the two block system? ___________________________________

Explanation / Answer

Momentum before collision = 0.03 . 240 = 7.2 kg m/s Velocity after collision = Momentum / mass = 7.2 / 2.91 = 2.47 m/s KE of moving pendulum = 1/2 . 2.91 . 2.47^2 = 8.9 J This energy is converted into height energy by the swing of the pendulum. Height raised must be KE / g . m = 31 cm

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