Question

In a system with masses mA = 1.60 kg and mB = 7.90 kg connected by a string over a frictionless pulley, what is the magnitude of the acceleration (in m/s²) of each object?

a. 3.9 m/s²
b. 6.5 m/s²
c. 9.1 m/s²
d. 12.3 m/s²

Answer 1

To find the acceleration in a system with masses mA = 1.60 kg and mB = 7.90 kg connected by a string over a frictionless pulley, we can use the following formula: a =
`(m_1 - m_2)/(m_1 + m_2)` × g. The magnitude of the acceleration is 6.5 m/s². So, the correct answer is b. 6.5 m/s².

Step-by-step explanation:

To find the acceleration in a system with masses connected by a string over a frictionless pulley, we can use the following formula:

a =
`(m_1 - m_2)/(m_1 + m_2)` × g

where:

- m₁ and m₂ are the masses,

- g is the acceleration due to gravity (approximately 9.8 m/s²).

Given
`\( m_A` = 1.60 kg and
`\( m_B` = 7.90 kg:

a =
`(1.60 - 7.90)/(1.60 + 7.90)` × 9.8 \]

a =
`(-6.30)/(9.50)` × 9.8 \]

Now, calculate the value:

a ≈ -6.53 m/s²

The negative sign indicates that the acceleration is upward for mass
`\( m_A \)` and downward for mass
`\( m_B \)`. If you are looking for the magnitude (absolute value) of the acceleration, it would be 6.53 m/s².

Among the given options, the closest one is:

b. 6.5 m/s²

So, the correct answer is b. 6.5 m/s².