Two blocks on a frictionless pully

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4) A block with mass rests on a frictionless horizontal table and is connected to a light cable that passes over a frictionless pulley and is then fastened to a hanging object with mass as shown in the figure. They start from rest and move 1.00 m before mass hits the floor.

(a) (5) Draw the free-body diagrams for each block including all vector forces. Note: No friction here.

(b) (5) Using Newton’s 2nd Law, find the sum of the component forces (i.e., x- and y-axis forces). Note the direction of the acceleration for each mass. Now find the acceleration.

(c) (5) Using a kinematic equation, find the speed of the blocks after they move 1.00 m.

(d) (5) Redraw the free-body diagram for mass if there was friction between it and the surface

In problem 4, use energy considerations to find the speed when the blocks move 1.00 m after starting from rest using the following steps.

1.) What is the initial speed for each mass?

2.) Find a simple expression for the change in kinetic energy of m1 and another one for m2Note: The final speeds of each mass must be the same since they are tied together. The final speed is the unknown.

3.) Find the change in potential energy of m1Hint: Is there any change in its height?

4.) Find the change in potential energy of m2.

5.) Use an important energy theorem to find .  Hint: Are there any frictional forces operating here?

asked Oct 27, 2014 in General

Treat m1 and m2 as one system and the external force making the acceleration is $m_2g$. So the acceleration is $\frac {m_2g}{m_1+m_2}$. The acceleration is identical (magnitude wise) for both blocks, which allows the finding of the tension force and frictional force (if any) -- use the free body diagrams.
With acceleration found, one can use $v_f^2-v_i^2=2a\Delta x$ to find the final velocity.
Using energy conservation, $mgh=\frac 12 (m_1+m_2)v^2$.