Question

The Atwood machine consists of two masses hanging from the ends of a rope that passes over a pulley. Assume that the rope and pulley are massless and that there is no friction in the pulley. If the masses have the values m1=21.1 kg and m2=12.9 kg, find the magnitude of their acceleration ???? and the tension T in the rope. Use ????=9.81 m/s2.

Answer 1

Answer:

$a=2.36\ m/s^2$

T=157.06 N

Explanation:

Given that

Mass of first block = 21.1 kg

Mass of second block = 12.9 kg

First mass is heavier than first that is why mass second first will go downward and mass second will go upward.

Given that pulley and string is mass  less that is why both mass will have same acceleration.So lets take their acceleration is 'a'.

So now from force equation

$m_1g-m_2g=(m_1+m_2)a$

21.1 x 9.81 - 12.9 x 9.81 =(21.1+12.9) a

$a=2.36\ m/s^2$

Lets tension in string is T

$m_1g-T=m_1a$

$T=m_1(g-a)$

T=21.1(9.81-2.36) N

T=157.06 N

Answer 2

The magnitude of their acceleration is 2.36m/s² while the tension in the rope is 157.06N.

From the information given, the following can be depicted:

• Mass of first block = 21.1kg
• Mas of second block = 12.9kg

The force equation can be used to calculate the magnitude of the acceleration which will go thus:

(21.1 × 9.81) - (12.9 × 9.81) = (21.1 + 12.9)a

(8.2 × 9.81) = 34a

a = (8.2 × 9.81) / 34

a = 2.36m/s².

Therefore, the tension will be:

T = m(g - a)

T = 21.1(9.81 - 2.36)N

T = 157.06N

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