Question

Determine the tension in the strings and accelerations of two blocks of mass 150 kg and 50 kg connected by a string
and a frictionless pulley of negligible weight

Answer 1

Answer:

The given system of two masses and a pulley can be represented as shown in the following figure:

Smaller mass, m

1

=8 kg

Larger mass,m

2

=12kg

Tension in the string=T

Mass m

2

, owing to its weight, moves downward with acceleration, and mass m

1

moves upward.

Applying Newton’s second law of motion to the system of each mass:

For mass m

1

:

The equation of motion can be written as:

T–m

1

g=ma… (i)

For mass m2:

The equation of motion can be written as:

m

2

g–T=m2a … (ii)

Adding equations (i) and (ii), we get:

(m2−m1)g=(m1+m2)a

a=

(m1+m2)

(m2−m1)g

....(iii)

=

(12+8)

(12−8)

×10=

20

4×10

=2ms−2

Therefore, the acceleration of the masses is 2 m/s2.

Substituting the value of a in equation (ii), we get:

m

2

g−T=m

2

(m

1

+m

2

)

(m

2

−m

1

)g

T=(m2−

(m1+m2)

(m

2

2

−m1m2)

g

=

(m

1

+m

2

)

2m

1

m

2

g

T=2×12×8×10/(12+8)

T=96N

Therefore, the tension in the string is 96 N.

Answer 2

The tension in the strings and accelerations of the two blocks are 7500N and 5m/s² respectively.

Given:-

Mass of heavier block = 150kg

Mass of lighter block = 50kg

To Find:-

The tension in the strings and accelerations of the two blocks.

Solution:-

We can easily find out the value of tension in the strings and accelerations of the two blocks by using these simple steps.

As

Mass of heavier block (m1) = 150kg

Mass of lighter block (m2) = 50kg

g = 10

Tension in the string (t) =?

Acceleration of the blocks (a) =?

So, according to the formula of tension in the string,

$t = \frac{2 \times m1 \times m2 \times g}{m1 + m2}$

on putting the values we get,

$t = \frac{2 \times 150 \times 50 \times 10}{150 + 50}$

$t = \frac{200 \times 150 \times 50}{200}$

$t = 150 \times 50$

$t = 7500N$

Now, for formula of acceleration of the blocks in a pulley block system,

$a = \frac{( m1 - m2)g}{m1 + m2}$

$a = \frac{(150 - 50) \times 10}{150 + 50}$

$a = \frac{100 \times 10}{200}$

$a = \frac{10}{2}$

$a = 5$

Hence, The tension in the strings and accelerations of the two blocks are 7500N and 5m/s² respectively.

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