Question

shows an acceleration-versus-force graph for three objects pulled by rubber bands. the mass of object b is 0.30 kg . what is the mass of object a?

Answer 1

If you know the mass of object B is 0.30 kg, and you have the slopes for both A and B from the graph, you can calculate the mass of object A with the below formula.

To determine the mass of object A from an acceleration-versus-force graph, we would follow these steps:

1. Find the slope of the line for object A: On an acceleration
`(\( a \))` versus force
`(\( F \))` graph, the slope of the line corresponding to each object is equal to the acceleration per unit force, which by Newton's second law
`(\( F = ma \)),` is equal to the inverse of the mass
`(\( (1)/(m) \))` of the object.

2. Use the slope to determine mass: Once you have the slope
`(\( s \))`, you can calculate the mass
`(\( m \))` of object A using the relationship
`\( s = (1)/(m) \), so \( m = (1)/(s) \).`

3. Compare the slope of object A to object B: If you know the mass of object B, and if you have the slopes for both A and B, you can use the ratio of the slopes to find the mass of object A because the slopes are inversely proportional to the masses:

`\[ (s_A)/(s_B) = (m_B)/(m_A) \]`

`\[ m_A = m_B * (s_B)/(s_A) \]`

4. Calculate the mass of object A: If you know the mass of object B is 0.30 kg, and you have the slopes for both A and B from the graph, you can calculate the mass of object A with the above formula.

Answer 2

The mass of object A can be calculated as Mass = 0.30 / 2.5 kg = 0.12 kg

how to determine the mass of object a?

The given mass of object B is 0.30 kg, and we aim to determine the mass of object A.

Newton's second law states that Force equals Mass multiplied by Acceleration, expressed as Acceleration = (1/Mass) × Force. Consequently, when graphing Acceleration against Force, the gradient represents 1/Mass.

For object B, the graph's gradient is 1, corresponding to a mass of 0.30 kg.

Considering object A, the graph's gradient is 2.5. Therefore, 1/Mass must be 2.5, implying that Mass = 1/2.5 in terms of 0.30 kg.

Thus, the mass of object A can be calculated as Mass = 0.30 / 2.5 kg = 0.12 kg.

See the missing graph below where object A is 1 and object B is 2