Two blocks of masses `m_(1)` and `m_(2)` interconnect with a spring of stiffness `K`, are kept on as smooth horizontal surface. Find out the ratio of velocity, displacement, kinetic energy and acceleration block with mass `m_(1)` of block with mass `m_(2)`.
Text Solution
Verified by Experts
Here `x` is the displacement, `v` is the speed, `p` is the mometum, a is the accelertion, `KE` is the kinetic energy, `F` is the force `(F_(ext))_("system")=0impliesvecp_(1)+vecp_(2)=0` `m_(1)v_(1)=m_(2)v_(2)impliesv_(1)/v_(2)=m_(2)/m_(1)` `m_(1)int_(0)^(1)v_(1)dt=m_(2)int_(0)^(1)v_(2)dt` where `t` is the time interval of motion of each block. `m_(1)x_(1)=m_(2)x_(2)impliesx_(1)/x_(2)=m_(2)/m_(1)` `(KE_(1))/(KE_(2))=(P_(1)^(2)//2m_(1))/(P_(1)^(2)//2m_(2))=m_(2)/m_(1)` (`:'p_(1)=p_(2))` `impliesF_(1)/F_(2)=(kx)/(kx)` where `x` is the deformation of the spring. `:. F_(1)/F_(2)=1=(m_(1)a_(1))/(m_(2)a_(2))=1impliesa_(1)/a_(2)=m_(2)/m_(1)`
Two blocks of masses m_(1) and m_(2) being connected with a light spring of stiffness k are driven with forces F_(1) and F_(2) on a smooth plane .find the value of spring force .
Two smooth blocks of mases m_(1) and m_(2) attached with an ideal spring of stiffness k and kept on hrozontal surface. If m_(1) is projected with a horizontal velocity v_(0) . Find the maximum compression of the spring.
Two block of masses m_(1) and m_(2) are connected as shown in the figure. The acceleration of the block m_(2) is:
Two blocks of masses m_(1) and m_(2) are connected by a massless spring and placed on smooth surface. The spring initially stretched and released. Then :
Two blocks of masses m_(1) and m_(2) , connected by a weightless spring of stiffness k rest on a smooth horizontal plane as shown in Fig. Block 2 is shifted a small distance x to the left and then released. Find the velocity of centre of mass of the system after block 1 breaks off the wall.
Two blocks of masses m_1 and m_2 are connected as shown in the figure. The acceleration of the block m_2 is :
A block of mass m is placed at rest on a smooth wedge of mass M placed at rest on a smooth horizontal surface. As the system is released
Two blocks of masses m_(1) and m_(2) are connected by a spring of stiffness k. The coefficient of friction between the blocks and the surface is mu . Find the minimum constant force F to be applied to m_(1) in order to just slide the mass m_(2) .
Two blocks of masses m and M connected by a light spring of stiffness k, are kept on a smooth horizontal surface as shown in figure. What should be the initial compression of the spring so that the system will be about to break off the surface, after releasing the block m_1 ?
Two block of masses m_(1) and m_(2) are placed side by side on a smooth horizontal surface as shown in fig. A horizontal force F is applied on the block . (a) Find the acceleration of each block. (b) Find the normal reaction between the two blocks.
CENGAGE PHYSICS ENGLISH-CENTRE OF MASS-INTEGER_TYPE
