A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m as shown in A horizontal force F is applied to one end of the rope. Find
(a) the acceleration of the rope and block
(b) the force that the rope exerts on the block
(c) the tension in the rope at its mid point

Answer

(a) `(F/(M+m))`
(b) `(MF)/(M+m)`
(c) `((2M+m))/(2(M+m))F`

Explanation

(a) Acceleration of system `a=F/(M+m)`
(b)
`T=Ma`
`T=(MF)/(M+m)`
(c) FBD of rope let 'T' be tension at mid point

`:. T'-T=m/2a,("For shaded portion of rope")`
`:. T'=T+m/2(F/(m+M))`
`=(MF)/((m+M))+(mF)/(2(m+M))`
`T' = ((2M+m)F)/(2(m+M))`