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saw5 [17]
1 year 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]1 year 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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Harlamova29_29 [7]

Answer:

38.0 m/s east

Explanation:

Momentum is conserved.

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

(0.311) (30.3) + (0.0570) (19.2) = (0.311) v₁ + (0.0570) v₂

10.52 = 0.311 v₁ + 0.0570 v₂

In an elastic collision, kinetic energy is conserved.

½ m₁u₁² + ½ m₂u₂² = ½ m₁v₁² + ½ m₂v₂²

m₁u₁² + m₂u₂² = m₁v₁² + m₂v₂²

(0.311) (30.3)² + (0.0570) (19.2)² = (0.311) v₁² + (0.0570) v₂²

306.5 = 0.311 v₁² + 0.0570 v₂²

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0.311 v₁ = 10.52 − 0.0570 v₂

v₁ = 33.82 − 0.1833 v₂

306.5 = 0.311 (33.82 − 0.1833 v₂)² + 0.0570 v₂²

306.5 = 0.311 (1144 − 12.40 v₂ + 0.03360 v₂²) + 0.0570 v₂²

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0 = 0.06745 v₂² − 3.856 v₂ + 49.16

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We know v₂ isn't 19.2 m/s, so v₂ = 38.0 m/s.

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