Question

a 0.8 kg wooden block is pulled by a force. the accelerometer data shows that the blocks acceleration is second time with the same force, but the mass is changed to 0.4 kg. which prediction should be made about the blocks acceleration?
a. it will be one - fourth as much.
b. it will be one - half as much.
c. it will be two times as much.
d. it will be four times as much.

Explanation:

Step1: Recall Newton's Second Law

Newton's second law is \( F = ma \), where \( F \) is force, \( m \) is mass, and \( a \) is acceleration. We can rearrange it to \( a=\frac{F}{m} \).

Step2: Analyze the initial and final states

Let the initial mass be \( m_1 = 0.8\space kg \) and the final mass be \( m_2 = 0.4\space kg \). The force \( F \) is the same in both cases, so \( F = m_1a_1=m_2a_2 \).

Step3: Find the ratio of accelerations

From \( m_1a_1=m_2a_2 \), we can solve for \( \frac{a_2}{a_1}=\frac{m_1}{m_2} \). Substituting \( m_1 = 0.8\space kg \) and \( m_2 = 0.4\space kg \), we get \( \frac{a_2}{a_1}=\frac{0.8}{0.4} = 2 \). So \( a_2 = 2a_1 \), meaning the acceleration will be two times as much.

Answer:

C. It will be two times as much.