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Chapter 7: Q. 36 (page 179)

The block of massM inFIGURE P7.36 slides on a frictionless surface. Find an expression for the tension in the string

Short Answer

Expert verified

Expression for tension isT=MmgM+m.

Step by step solution

01

Given information

"M" and "m" are the mass of the block.

02

Explanation

Force due to gravity on the block of mass m is mg.

According to the Newton law

Fnet=Mtotal×a

Fnetis the net force on mass m.

Mtotalis the total mass of both the blocks.

a is the acceleration of the mass m.

localid="1649252977169" mg=M+maa=mgM+m

If the block mass of m is moving downwards then the tension in the spring is

localid="1649253032356" T=mg-ma⋯⋯(1)

According to the Newton law

Fnet=Mtotal×a

where Fnet and a is the net force and acceleration of the mass m respectively.

mg=M+maa=mgM+m

Substitute the value of ain the equation (1)

localid="1649253219152" role="math" T=mg-m2gM+mT=mgM+m-m2gM+mT=Mmg+m2g-m2gM+mT=MmgM+m

The tension in the string is T=MmgM+m

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