CBSE Class 11-science Answered
A block of mass m is placed on a wedge as
shown. Find difference between maximum and
minimum (a(max) – a(min) ) horizontal rightward
acceleration of wedge for which block remains
at rest with respect to wedge.
(A) 10g/9
(B) g/9
(C) g
(D) None of these
Asked by sahuaryanbro1.0 | 01 Jan, 2023, 22:17: PM
Expert Answer
Fig.(1) shows the forces acting on block of mass m . Weight mg is resolved as ( mgcos37 ) normal to inclined surface
and ( m g sin37 ) parallel to inclined surface. Where m is mass of block and g is acceleration due to gravity.
When we observe moving wedge and block and if block does not slip, then
the block experience a psuedo force ( m a ) , where a is accceleration of system .
This pseudo force also resolved as ( m a cos37 ) parallel to inclined plane and ( m a sin37) normal to inclined surface.
Normal reaction force N = m ( g cos37 + a sin37 )
friction force μN = (1/3) m ( g cos37 + a sin37 )
where μ =1/3 is friction coefficient
Condition for sliding the block downwards is
( mg sin37 - ma cos37 ) ≥ μN
( mg sin37 - ma cos37 ) ≥ (1/3) m ( g cos37 + a sin37 )
Acceleration a in above expression is minimum acceleration amin of system
we get from above expression , amin = ( g/3 )
-------------------------------------------------------------------
When system acceleration exceeds g/3 , friction force increases because friction depends on normal force N
and normal force N depends on system acceleration a .
if pseudo force component ( ma cos37 ) excceds weight component ( m g sin37) then net force directed upwards
and friction force will be downwards inorder to prevent the block sliding upward.
This situation is shown in fig.(2)
Now, condition for sliding the block upwards is
(ma cos37 - mg sin37 ) ≥ μN
( ma cos37 - mg sin37 ) ≥ (1/3) m ( g cos37 + a sin37 )
Acceleration a in above expression is maximum acceleration amax of system
we get from above expression , amax = ( 13/3 ) g
----------------------------------------------
Difference ( amax - amin ) = [ (13/3) - (1/3) ] g = 4g
Answered by Thiyagarajan K | 02 Jan, 2023, 22:37: PM
Concept Videos
-
Common Forces in Mechanics
This video explains body in equilibrium and resolving forces acting on a bo... -
Common Forces in Mechanics
This video explains the common forces acting on an object in the study of m... -
Common Forces in Mechanics
This video contains practice questions on body in equilibrium, restoring fo...
CBSE 11-science - Physics
Asked by sahuaryanbro1.0 | 01 Jan, 2023, 22:17: PM
ANSWERED BY EXPERTCBSE 11-science - Physics
Asked by kashyspalbert91 | 11 Mar, 2022, 16:11: PM
ANSWERED BY EXPERTCBSE 11-science - Physics
Asked by Sainajena311 | 23 Oct, 2019, 21:39: PM
ANSWERED BY EXPERTCBSE 11-science - Physics
Asked by Topperlearning User | 05 Jun, 2014, 14:29: PM
ANSWERED BY EXPERTCBSE 11-science - Physics
Asked by Topperlearning User | 04 Jun, 2014, 13:23: PM
ANSWERED BY EXPERTCBSE 11-science - Physics
Asked by Topperlearning User | 04 Jun, 2014, 13:23: PM
ANSWERED BY EXPERTCBSE 11-science - Physics
Asked by Topperlearning User | 05 Jun, 2014, 15:48: PM
ANSWERED BY EXPERTCBSE 11-science - Physics
Asked by Topperlearning User | 05 Jun, 2014, 15:54: PM
ANSWERED BY EXPERTCBSE 11-science - Physics
Asked by Topperlearning User | 05 Jun, 2014, 15:55: PM
ANSWERED BY EXPERTCBSE 11-science - Physics
Asked by Topperlearning User | 05 Jun, 2014, 16:04: PM
ANSWERED BY EXPERT