P Lab Atwood

Why is an Atwood Machine useful for measuring the acceleration of falling objects compared to simply dropping a mass in free fall?

In free fall, objects accelerate quickly due to gravity, making it difficult to measure time accurately. An Atwood Machine slows down the motion by distributing the force between two masses and a pulley, making it easier to measure the acceleration over time.

In the Atwood Machine, what assumption allows us to say that the tension is the same on both sides of the string?

We assume the pulley is frictionless and the string is massless and inextensible. This allows us to treat the tension throughout the string as uniform, so T1=T2=T

Write the equation for the net acceleration of the system in terms of m1, m2 and g

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

What would happen to the acceleration if both masses were equal? Explain why.

If m1=m2​, then the numerator of the acceleration equation becomes 0:

a = (m2 - m1/ m1 + m2) x g g=0

This means the system would not accelerate — it would stay at rest or move at constant velocity if already moving.

How does increasing the mass difference between m1m_1m1​ and m2m_2m2​ affect the system’s acceleration?

Increasing the mass difference (m2−m1) increases the numerator in the acceleration equation, which increases the system's acceleration. The larger the difference, the faster the heavier mass falls.

Given:

• m1=0.050 kg, m2=0.060 kg

• Distance d=0.5 m

• Time t=1.10 s

Calculate experimental acceleration

0.826 m/s²

Given:

• m1=0.050 kg, m2=0.060 kg

• Distance d=0.5 m

• Time t=1.10 s

Calculate experimental gravity g

9.09 m/s²

Compare with 9.8 m/s². What could explain the difference?
The value is a bit lower than 9.8 m/s². Possible reasons:

• Friction in the pulley

• Air resistance

• Delay in reaction time when measuring

• Uneven string tension or pulley alignment

How does mass difference affect acceleration and accuracy?

• Larger mass differences → higher acceleration, making it easier to measure time accurately.

• Smaller differences → lower acceleration, making the system more sensitive to friction, reaction time, and measurement error.

• The closer the mass difference is to 0, the less reliable the calculated gravity value becomes.