A block with mass m_A is placed on an inclined plane with slope angle a and is c

Question

A block with mass m_A is placed on an inclined plane with slope angle a and is connected to a second hinging block with mass m_B > m_A by a mass less cord passing over a small, friction less pulley (see figure). The coefficient of kinetic friction between mass m_A and the incline is negligible. Initially the masses are at rest, with mass m_A at the bottom of the incline and mass m_B a height h above the table supporting the incline (see figure). As the masses are released: Find how high (vertically) has mass mA moved when mass mB reaches the table. Explain. Find the speed v of mass mB just before hitting the table. If the mass of the pulley is not negligible, will this final speed be bigger or smaller? Explain. Write your results in terms of mA. mB, a, h. g. Check the units/dimensions for each answer. MAKE SURE TO SET YOUR AXES OR YUO WILL LOOSE POINTS!

Explanation / Answer

a)
mB moves down a distance h
mA also moves a distance h along the incline since they are connected by rope
height moved verticaly = h*sin alpha
Answer: h*sin alpha

b)
decrease in potential energy of B - increase in potential energy of A = kinetic enrgy
mB*g*h - mA*g*(h*sin alpha) = 0.5*(mA+mB)*v^2
v = sqrt [ 2*{mB*g*h - mA*g*(h*sin alpha)} / (mA+mB)]

c)
When pelley is not geligible mass,
decrease in potential energy of B - increase in potential energy of A = kinetic enrgy of mass + kinetic energy of puller

so kinetic energy of mass will be less
hence velocity will be less

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