Question

a group of students are measuring the acceleration of the atwood machine pictured above. then one student suggests that they use a 4 kg and 5 kg mass. how will the acceleration of the system with 4 kg and 5 kg masses compare to the original system?
a the acceleration of the new system will be smaller because the total mass of the system is larger
b the acceleration of the new system will be smaller because the 4 kg mass has more weight
c the acceleration of the new system will be larger because the total mass of the system is larger
d the acceleration of the new system will be larger because the 5 kg mass has more weight

Explanation:

For an Atwood machine, the acceleration \( a=\frac{(m_2 - m_1)g}{m_1 + m_2} \) (where \( m_2>m_1 \), \( g \) is gravitational acceleration). Original masses: let's assume original is 3 kg and 2 kg. Total mass \( m_{total1}=3 + 2=5 \) kg, net force \( F_{net1}=(3 - 2)g = g \). New masses: 5 kg and 4 kg. Total mass \( m_{total2}=5 + 4 = 9 \) kg, net force \( F_{net2}=(5 - 4)g=g \). Acceleration formula: \( a=\frac{F_{net}}{m_{total}} \). Since \( F_{net} \) is same (both have a mass difference of 1 kg, so net force \( (m_2 - m_1)g \) is \( g \) in both cases), but \( m_{total2}(9\space kg)>m_{total1}(5\space kg) \), so \( a_2=\frac{g}{9} \), \( a_1=\frac{g}{5} \). So new acceleration is smaller because total mass is larger. Option A says "The acceleration of the new system will be smaller because the total mass of the system is larger" which matches. Option B is wrong because 4 kg is smaller than 5 kg, so 4 kg has less weight. Option C is wrong as larger total mass leads to smaller acceleration (inverse relationship when net force is constant). Option D is wrong as 5 kg has more weight, but the acceleration depends on mass difference and total mass, not just the weight of the larger mass. So correct is A.

Answer:

A. The acceleration of the new system will be smaller because the total mass of the system is larger