Rosa uses a spring scale to pull a cart along a track for 2 meters. The spring scale shows the force exerted on the cart while being pulled. She uses metal plates to vary the mass of the cart, and motion sensors to calculate the average speed and acceleration of the cart.

She records the results in a table.

Rosa claims that the force needed to accelerate an object is proportional to the mass of the object. Which statement BEST supports or disproves Rosa’s claim using the data from the table?

A- Rosa’s claim is false. When the mass of the cart increases by 1.0 kg, the force on the cart increases by more than 1.0 kilogram.

B- Rosa’s claim is false. Even though the mass and the force increase in each trial, the acceleration of the object remains the same.

C-Rosa’s claim is true. The acceleration for each trial is the same. Doubling the mass of the cart causes the force to double in order to maintain the same rate of acceleration.

D-Rosa’s claim is true. Each time the mass increases by 1.0 or 2.0 kilograms, the force increases by 1.0 or 2.0 newtons respectively. This causes the rate of acceleration to remain constant.

Rosa’s claim is true. The acceleration for each trial is the same. Doubling the mass of the cart causes the force to double in order to maintain the same rate of acceleration.

According to Newton's second law of motion, the force applied to an object is directly proportional to the product of the mass and acceleration of the object.

F = ma

[tex]a = \frac{F}{m} \\\\\frac{F_1}{m_1} = \frac{F_2}{m_2} \\\\\frac{2}{1} = \frac{F_2}{2} \\\\F_2 = 4 \ N \\\\when \ the \ mass \ increases \ by \ 2\\\\m_1 = 2 \ kg,\ \ m_2 = 2(m_1) = 2(2) = 4 \ kg\\\\F_1 = 4 \ N, \ \ F_2 = 2(F_1) = 2(4) = 8 \ N[/tex]

Thus, we can conclude that from the table, Rosa’s claim is true. The acceleration for each trial is the same. Doubling the mass of the cart causes the force to double in order to maintain the same rate of acceleration.

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