A group of students conducted a physics experiment to study the relationship between the m… — ACT

A group of students conducted a physics experiment to study the relationship between the mass of a glider and its acceleration on a horizontal air track. A constant net force was applied to the glider during all trials. The students observed that the acceleration of the glider, $a$ , is inversely proportional to its mass, $m$ . During Trial 1, a glider with a mass of $0.20\text{ kg}$ was measured to have an acceleration of $5.0\text{ m/s}^2$ . During Trial 2, a different glider was used under the same constant net force. If the mass of the glider in Trial 2 is $0.50\text{ kg}$ , what is the acceleration of the glider, in $\text{m/s}^2$ ?

Answer: 2 m/s^2

Answer

The acceleration of the glider in Trial 2 is 2.0 m/s^2.

Since acceleration is inversely proportional to mass, their product remains constant under a constant net force. Using the data from Trial 1, the constant is calculated as

0.20\text{ kg} \times 5.0\text{ m/s}^2 = 1.0\text{ N}

. In Trial 2, with a mass of

0.50\text{ kg}

, the acceleration is found by dividing the constant by the new mass:

1.0 / 0.50 = 2.0\text{ m/s}^2

Step-by-Step Solution

Set up the inverse proportionality equation.

a \times m = k

Since acceleration is inversely proportional to mass, their product must equal a constant value.

Calculate the constant of proportionality using Trial 1 data.

k = 1.0

Substitute

m = 0.20\text{ kg}

and

a = 5.0\text{ m/s}^2

into the equation:

5.0 \times 0.20 = 1.0

Calculate the new acceleration for Trial 2.

a_2 = 2.0\text{ m/s}^2

Substitute the constant

k = 1.0

and the new mass

m_2 = 0.50\text{ kg}

into the equation:

a_2 \times 0.50 = 1.0

, so

a_2 = 2.0

Key Concept

Inverse proportionality relates two variables such that their product is constant. If one variable increases by a factor, the other must decrease by the same factor.

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