High School

In the Atwood machine shown below, [tex]m_1 = 2.00 \, \text{kg}[/tex] and [tex]m_2 = 5.60 \, \text{kg}[/tex]. The masses of the pulley and string are negligible by comparison. The pulley turns without friction and the string does not stretch. The lighter object is released with a sharp push that sets it into motion at [tex]v_i = 2.15 \, \text{m/s}[/tex] downward.

How far will [tex]m_1[/tex] descend below its initial level?

A. None
B. 12.2 cm
C. 97.6 cm
D. 24.4 cm
E. 48.8 cm

Answer :

Final answer:

In an Atwood machine, to find how far the lighter mass will descend, we calculate the system's acceleration and use it along with the initial velocity in a kinematic equation to find the displacement.

Explanation:

To solve the problem of how far mass m1 will descend in an Atwood machine, we must first calculate the acceleration of the system. We can use the following equation of motion due to net force acting on the system:

a = g(m2 - m1) / (m1 + m2)

Where
a is the acceleration,
g is the acceleration due to gravity (9.81 m/s2), m1 is the mass of the lighter object, and m2 is the mass of the heavier object. Once we have the acceleration, we can find the displacement (d) using the kinematic equation:

d = vi2 / (2a)

Where
vi is the initial velocity and
a is the acceleration we calculated. By substituting the given initial velocity and calculated acceleration, we can find the displacement that m1 will descend below its initial level.

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