The heavier block is an Atwood machine that has a mass twice that of the lighter one. The tension in the string is 16.0N when the system is set into the motion. Find the decrease in the gravitational potential energy during the first second after the system is released from rest.

Tension is a force along the length of a medium, especially a force carried by a flexible medium, such as a rope or cable. Tension can be defined as an action-reaction pair of forces acting at each end of the said elements.

Tension formula is articulated as

T=mg+ma

Where,

T= tension (N or kg-m/s2)

g = acceleration due to gravity (9.8 m/s2)

m =Mass of the body

a = Acceleration of the moving body

If the body is travelling upward, the tension will be T = mg+ ma
If the body is travelling downward, the tension will be T = mg – ma
If the tension is equivalent to the weight of body T = mg

Solution

Given that,

Tension T = 16.0 N

Find out

We have to determine the decrease in the gravitational potential energy during the first second after the system is released from rest.

Solution

We know that tension is given by

The tension on an object is equal to the product of the mass of the object and gravitational force added to the product of the mass and acceleration. Mathematically,
T = mg + ma

T−2mg+2ma=0….(i)

T−mg−ma=0….(ii)

From the equations we can say that:
3ma−mg=0

g=3a

a=g/3

On substituting the value in equation (ii) we get
T−3ma−ma=0
⇒T=4ma
⇒a=T/ 4m

From the equation of motion, we get

s=ut+1/2at2

=>s=0+1/2×T4m×(1)

s=16/ 8m
Hence s=2m

Change in the height of the block will be:
Δh=s
The net mass as per the given condition
2m−m=m

The decrease of the potential energy is given as:
P.E.=mgΔh

P.E.=m×9.8×2/m
⇒P.E.=19.6J
Hence, the decreased potential energy is 19.6 J.

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