Question

an object has an acceleration of 12.0 m/s/s. if the mass of this object were halved (i.e., reduced to one - half the original value) (with no change in its net force), then its new acceleration would be ______ m/s/s.
new acceleration (in m/s/s)

Explanation:

Step1: Use Newton's second law

Newton's second law is \(F = ma\). Let the original mass be \(m_1\), original acceleration be \(a_1=12.0\ m/s^2\), so \(F = m_1\times12.0\).

Step2: Analyze the new - mass situation

The new mass \(m_2=\frac{1}{2}m_1\), and the net force \(F\) remains the same. Using \(F = m_2a_2\), substitute \(m_2=\frac{1}{2}m_1\) and \(F = m_1\times12.0\) into \(F = m_2a_2\). We get \(m_1\times12.0=\frac{1}{2}m_1\times a_2\).

Step3: Solve for the new acceleration

Cancel out \(m_1\) (since \(m_1
eq0\)) from both sides of the equation \(m_1\times12.0=\frac{1}{2}m_1\times a_2\). Then \(a_2 = 2\times12.0\).

Answer:

\(24.0\)