Question

an object has an acceleration of 18.0 m/s/s. if the net force was doubled and the mass was one - third the original value, then the new acceleration would be ______ m/s/s.
new acceleration (in m/s/s)

Explanation:

Step1: Recall Newton's second law

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

Step2: Analyze the new - force and new - mass

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

Step3: Calculate the new acceleration

Using \(a=\frac{F}{m}\), the new acceleration \(a_2=\frac{F_2}{m_2}\). Substitute \(F_2 = 2F_1\) and \(m_2=\frac{1}{3}m_1\) into the formula: \(a_2=\frac{2F_1}{\frac{1}{3}m_1}\).
Since \(a_1=\frac{F_1}{m_1} = 18.0\), then \(a_2=2\times3\times\frac{F_1}{m_1}\).

Step4: Find the value of the new acceleration

\(a_2 = 6a_1\). Substitute \(a_1 = 18.0\) into the formula: \(a_2=6\times18.0=108\).

Answer:

\(108\)