Question

an object has an acceleration of 18.0 m/s/s. if the net force was tripled and the mass were halved, then the new acceleration would be ______ m/s/s.

Explanation:

Step1: Recall Newton's second law

Newton's second law is \(F = ma\), so \(a=\frac{F}{m}\). Initially, \(a_1 = 18.0\ m/s^2=\frac{F_1}{m_1}\).

Step2: Analyze the new force and mass

The new force \(F_2 = 3F_1\), and the new mass \(m_2=\frac{1}{2}m_1\).

Step3: Calculate the new acceleration

Using \(a=\frac{F}{m}\), the new acceleration \(a_2=\frac{F_2}{m_2}\). Substitute \(F_2 = 3F_1\) and \(m_2=\frac{1}{2}m_1\) into the formula: \(a_2=\frac{3F_1}{\frac{1}{2}m_1}\). Since \(a_1=\frac{F_1}{m_1} = 18.0\ m/s^2\), then \(a_2=3\times2\times\frac{F_1}{m_1}\).

Step4: Substitute the initial acceleration value

\(a_2 = 6a_1\). Substitute \(a_1 = 18.0\ m/s^2\) into the formula: \(a_2=6\times18.0\ m/s^2\).

Answer:

\(108\)