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saw5 [17]
2 years ago
7

Two objects (45.0 and 21.0 kg) are connected by a massless string that passes over a massless, frictionless pulley. The pulley h

angs from the ceiling. Find
(a) the acceleration of the objects and
(b) the tension in the string.
Physics
1 answer:
Oksanka [162]2 years ago
4 0

a) The acceleration of the objects is 3.56 m/s^2

b) The tension in the string is 280.8 N

Explanation:

a)

We start by writing the equations of motion for the two masses attached to the pulley.

For the heavier mass, we have:

m_1 g - T = m_1 a (1)

where

m_1 = 45.0 kg is the mass

g=9.8 m/s^2 is the acceleration of gravity

T is the tension in the string

a is the acceleration of the system (here we assumed that the heavier mass accelerates downward)

For the lighter mass, we have

T-m_2 g = m_2 a (2)

where

T is the tension in the string

m_2 = 21.0 kg is the mass

g=9.8 m/s^2 is the acceleration of gravity

a is the acceleration of the system (here we assumed that the lighter mass accelerates upward)

From (1) we get

T=m_1g - m_1 a

And substituting into (2),

(m_1 g - m_1 a)-m_2 g = m_2 a\\(m_1 -m_2)g  = (m_1+m_2)a\\a=\frac{m_1 - m_2}{m_1+m_2}g=\frac{45-21}{45+21}(9.8)=3.56 m/s^2

b)

From the previous part of the problem we got an expression for the tension in the string:

T=m_1g - m_1 a

Where we have

m_1 = 45.0 kg

g=9.8 m/s^2

a=3.56 m/s^2 is the acceleration, found in part a)

Susbtituting, we find

T=(45.0)(9.8)-(45.0)(3.56)=280.8 N

Learn more about forces and acceleration:

brainly.com/question/11411375

brainly.com/question/1971321

brainly.com/question/2286502

brainly.com/question/2562700

#LearnwithBrainly

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