Calculate the acceleration of the system, tension in the string and thrust on the pulley in terms of g for the
situation shown in following diagram.
Answers
The value of acceleration of the system, tension in the string and thrust on the pulley in terms of g for the situation are g/3 m/s², 10g/3 N and √2×10g/3 N respectively.
Given:-
Mass of heavier body = 10kg
Mass of lighter body = 5kg
Tension in the rope = T
Acceleration of the system = a
To Find:-
The value of acceleration of the system, tension in the string and thrust on the pulley in terms of g for the situation.
Solution:-
We can easily calculate the The value of acceleration of the system, tension in the string and thrust on the pulley in terms of g for the situation by using these simple steps.
As
Mass of heavier body (m1) = 10kg
Mass of lighter body (m2) = 5kg
Tension in the rope = T
Acceleration of the system = a
According to the formula for lighter mass,
F(net) = m×a
i.e. (m×g) - T = m×a
5g - T = 5a
For heavier mass,
T - 0 = 10a
T = 10a
putting this value of T in above equation,
5g - 10a = 5a
5g = 5a + 10a
5g = 15a
a = 5g/15
a = g/3
Now, Tension in the string = T
T = 10a
T = 10 × g/3
T = 10g/3 N
Now, Thrust on the pulley = F
F² = T² + T²
F² = 2T²
on taking root both sides,
F = √2T
F = √2 × 10g/3 N
Hence, The value of acceleration of the system, tension in the string and thrust on the pulley in terms of g for the situation are g/3 m/s², 10g/3 N and √2×10g/3 N respectively.
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Answer:
Given information:
Mass of heavier body = 10kg
Mass of lighter body = 5kg
Tension in the rope = T
Acceleration of the system = a
To Locate:
The system's acceleration, string tension, and pulley thrust values, all expressed in terms of g.
Result:
By following these easy methods, we can quickly determine the system's acceleration, the string's tension, and the pulley's push in terms of g.
Mass of heavier body (m1) = 10kg
Mass of lighter body (m2) = 5kg
Tension in the rope = T
Acceleration of the system = a
According to the formula for lighter mass,
F(net) = m×a
i.e. (m×g) - T = m×a
5g - T = 5a
For heavier mass,
T - 0 = 10a
T = 10a
Putting this value of T in above equation,
5g - 10a = 5a
5g = 5a + 10a
5g = 15a
a = 5g/15
a = g/3
Now, Tension in the string = T
T = 10a
T = 10 × g/3
T = 10g/3 N
Now, Thrust on the pulley = F
F² = T² + T²
F² = 2T²
On taking root both sides,
F = √2T
F = √2 × 10g/3 N
As a result, the system's acceleration, string tension, and pulley thrust values for the circumstance are, respectively, g/3 m/s2, 10g/3 N, and 210g/3 N.
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