A pulley fixed to the ceiling carried a thread with bodies of masses `m_(1)` and `m_(2)` attached to its ends. The mases of the pulley and the thread are negligible and friction is absent. Find the acceleration of the centre of mass of this system.
Text Solution
Verified by Experts
Let us assume that `m_(2)gtm_(1)`. We can see that the masses have equal and opposite acceleration of the same magnitude. `a=(m_(2)-m_(1))/(m_(2)+m_(1))g` and tension in string is `T=(2m_(1)m_(2)g)/(m_(2)+m_(1))` Taking downward direction as positive `a_(1)=-,a_(2)=+a` `a_(CM)=(m_(1)a_(1)+m_(2)a_(2))/(m_(1)+m_(2))=((m_(2)-m_(1))a)/(m_(2)+m_(1))` substituting for the value of a we have `a_(CM)=((m_(2)-m_(1))/(m_(2)+m_(1)))^(2) g` Alternative method: `a_(CM)=F_(ext)/(m_(1)+m_(2))=((m_(1)g+m_(2)g)-2T)/(m_(1)+m_(2))=g-(2T)/(m_(1)+m_(2))` `=g-(4m_(1)m_(2)g)/((m_(2)+m_(1))^(2))=((m_(2)-m_(1))/(m_(2)+m_(1)))^(2)g` (downwards)
A pulley fixed to the ceiling carries a thread with bodies of masses m_(1) and m_(2) attached at its ends. The masses of the pulley and thread are negligible, friction is absent. Find the acceleration of the centre of mass (a_("cm")) of this system.
A pulley fixed to the ceiling carries a thread with bodies of masses m_1 and m_2 attached to its ends. The masses of the pulley and the thread are negligible, friction is absent. Find the acceleration w_C of the centre of inertia of this system.
A pulley fixed to the ceiling carries a string with blocks of mass m and 3m attached to its ends. The masses of string and pulley are negligible .When the system is released, its center of mass moves with what acceleration
In the arrangement shown in fig the bodies have masses m_(0), m_(1) and m_(2) the friction is absent the masses of pulleys and the threads are negligible find the acceleration of the body m_(1)
Two bodies with masses m_1 and m_2(m_1gtm_2) are joined by a string passing over fixed pulley. Assume masses of the pulley and thread negligible. Then the acceleration of the centre of mass of the system (m_1+m_2) is
In the arrangement shown in the figure, the blocks have masses 3m,m and 2m , the friction is absent, the masses of the pulleys and the threads are negligible. Find the acceleration of mass 3m .
In the arrangement shown in figure the bodies have masses m_0 , m_1 , m_2 , the friction is absent, the masses of the pulleys and the threads are negligible. Find the acceleration of the body m_1 . Look into possible cases.
Two blocks of masses 6 kg and 4 kg are attached to the two ends of a massless string passing over a smooth fixed pulley. if the system is released, the acceleration of the centre of mass of the system will be
In the arrangement shown in figure the masses m of the bar and M of the wedge, as well as the wedge angle alpha , are known. The masses of the pulley and the thread are negligible. The friction is absent. Find the acceleration of the wedge M.
In the arrangement of figure the masses m_0 , m_1 , and m_2 of bodies are equal, the masses of the pulley and the threads are negligible, and there is no friction in the pulley. Find the acceleration w with which the body m_0 comes down, and the tension of the thread binding together the bodies m_1 and m_2 , if the coefficient of friction between these bodies and the horizontal surface is equal to k. Consider possible cases.
