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CBSE Class 11-science Answered

Two blocks A and B of masses 6 Kg and 3 Kg are moving with constant speed on a rough surface
inclined at an angle 30° with respect to horizontal. Find
(a) Coefficient of kinetic friction, assuming it to be same for both the block
(b) Tension in the String

 

Asked by juhi.mundheda | 08 Oct, 2020, 07:52: AM
Expert Answer
Figure shows two blocks connected by string moving on the inclined plane with constant speed .
 
Weight of each block mg is resolved into two components
(i) mg cos30 perpendicular to inclined plane that gives equal normal force  and
(ii) parallel to inclined plane mgsin30 that gives force to slide down the block.
 
Friction force μN = μmgcos30 is acting against the direction of motion .
 
Tension forces T are acting in the string as shown in figure.
 
Since it is given that blocks are moving with constant speed, net force acting on each block is zero.
 
Hence by applying Newton's second law on each block, we get
 
T + m1 g sin30 = μ m1 g cos30   ....................(1)
 
T + μ m2 g cos30 = m2 g sin30  ....................(2)
 
By eliminating T from above equation , we get μ = tan30 = 1/√3 = 0.58 as explained below
 
Subtract eqn.(2) from eqn.(1), to get ,   m1 g sin30  - μ m2 g cos30 = μ m1 g cos30 -  m2 g sin30 
 
from above equation , we get μ = tan30 
 
By substituting μ = tan30  in any one of above equation, we get T = 0
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