Question

question 17 (1 point)
if you push a 4.0-kg mass with the same force that you push a 10-kg mass from rest,
the 10-kg mass accelerates 2.5 times faster than the 4.0-kg mass.
the 4.0-kg mass accelerates 2.5 times faster than the 10-kg mass.
both masses accelerate at the same rate.
none of the above is true.

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. Rearranging for acceleration, we get \( a=\frac{F}{m} \).

Step2: Analyze the given forces and masses

Let the force applied to both masses be \( F \). For the \( 4.0 - \text{kg} \) mass, \( m_1 = 4.0\space\text{kg} \), so its acceleration \( a_1=\frac{F}{4.0} \). For the \( 10 - \text{kg} \) mass, \( m_2 = 10\space\text{kg} \), so its acceleration \( a_2=\frac{F}{10} \).

Step3: Find the ratio of accelerations

To find how many times faster one accelerates than the other, we take the ratio \( \frac{a_1}{a_2}=\frac{\frac{F}{4.0}}{\frac{F}{10}} \). The \( F \) cancels out, and we have \( \frac{a_1}{a_2}=\frac{10}{4.0}=2.5 \). So \( a_1 = 2.5a_2 \), meaning the \( 4.0 - \text{kg} \) mass accelerates 2.5 times faster than the \( 10 - \text{kg} \) mass.

Answer:

the 4.0-kg mass accelerates 2.5 times faster than the 10-kg mass.