In the figure, M2 has more mass than M1 and M1 has more mass than M3. The questi

Question

In the figure, M2 has more mass than M1 and M1 has more mass than M3. The questions refer to the magnitudes of tensions and weights.

There is friction between the horizontal plane and M2 (?k ? 0). M2 is observed to travel at a constant speed. Assume that the pulleys are frictionless and have negligible mass. Select the appropriate statements to complete the following sentences.

TrueFalseGreater thanLess thanEqual to T3 is ... T2.
TrueFalseGreater thanLess thanEqual to M1g is ... T1.
TrueFalseGreater thanLess thanEqual to The magnitude of the net force on M2 is T2 - T3.
TrueFalseGreater thanLess thanEqual to M1 accelerates downwards.
TrueFalseGreater thanLess thanEqual to T4 is ... M3g
TrueFalseGreater thanLess thanEqual to T2 is ... T1.

In the figure, M2 has more mass than M1 and M1 has more mass than M3. The questions refer to the magnitudes of tensions and weights. There is friction between the horizontal plane and M2 (?k ? 0). M2 is observed to travel at a constant speed. Assume that the pulleys are frictionless and have negligible mass. Select the appropriate statements to complete the following sentences. T3 is ... T2. M1g is ... T1. The magnitude of the net force on M2 is T2 - T3. M1 accelerates downwards. T4 is ... M3g T2 is ... T1.

Explanation / Answer

let M2 is moving towards right.
friction coefficient=k
if M2 is moving at constant speed ,then M1 and M3 are also moving at constant speed.
so acceleration of the system is zero.
As pulley is frictionless and mass less,the tension in the cord will remain the same.
so
T1=T2 and
T3=T4
hence for the mass M1,
T1=M1*g...(1)
for M2,
T3=T2+k*M2*g...(2)
or T3=T1+k*M2*g=M1*g+M2*g...(3)
for mass M3,
T4=M3*g.(4)
as T4=T3
T3=(M1+k*M2)*g=M3*g
which is not possible as M2>M1>M3
so our assumption is wrong
that is M2 is moving to the left.
hence the force equations will become:-
hence for the mass M1,
T1=M1*g...(5)
for M2,
T2=T3+k*M2*g...(6)
or T3=T1-k*M2*g=M1*g-k*M2*g...(7)
for mass M3,
T4=M3*g.(8)
as T4=T3

M3*g=(M1-k*M2)*g

so M3=M1-k*M2.....(9)

answers to the questions...

(a.)

from equation 6,it is seen that T2=T3+k*M2*g

hence T2 is greater than T3.

(b.)from equation 5,M1*g=T1

(c.)from 6,magnitude of net force on M2 is zero.as it is moving in constant speed.the statement is false.

(d.)there is zero force on M1.

statement is false.

(e)T4=M3*g(from equation 8)

(f)T2 is equal to T1.

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