Question
A pail filled with sand has a total mass of $$60\,kg.$$ A crane is lowering it such that it has an initial downward acceleration of $$1.5\,m/{s^2}.$$ A hole in the pail allows sand to leak out. If the force exerted by the crane on the pail does not change, what mass of sand must leak out before the downward acceleration decreases to zero?
A.
$$9.2\,kg$$
B.
$$20\,kg$$
C.
$$40\,kg$$
D.
$$51\,kg$$
Answer :
$$9.2\,kg$$
Solution :
Free body diagram at start
Free body diagram when $$a = 0$$
$$\eqalign{ & {m_1}g - {F_c} = {m_1}a;{F_c} = {m_1}\left( {g - a} \right) \cr & {F_c} - {m_2}g = 0;{F_c} = {m_2}g \cr & {m_1}\left( {g - a} \right) = {m_2}g \cr & {m_2} = \frac{{{m_1}\left( {g - a} \right)}}{g} = 50.8\,kg; \cr & \Delta m = 9.2\,kg \cr} $$
Free body diagram at start
Free body diagram when $$a = 0$$
$$\eqalign{ & {m_1}g - {F_c} = {m_1}a;{F_c} = {m_1}\left( {g - a} \right) \cr & {F_c} - {m_2}g = 0;{F_c} = {m_2}g \cr & {m_1}\left( {g - a} \right) = {m_2}g \cr & {m_2} = \frac{{{m_1}\left( {g - a} \right)}}{g} = 50.8\,kg; \cr & \Delta m = 9.2\,kg \cr} $$
