2. effect of mass on acceleration. a student exerts the same net force on two carts. cart a has a mass of 2…

Explanation:

Step1: Recall Newton's second - law

Newton's second - law is $F = ma$, where $F$ is the net force, $m$ is the mass, and $a$ is the acceleration. We can rewrite it as $a=\frac{F}{m}$.

Step2: Analyze the acceleration of Cart A

Let the net force on both carts be $F$. For Cart A with $m_A = 2\ kg$, the acceleration $a_A=\frac{F}{m_A}=\frac{F}{2}$.

Step3: Analyze the acceleration of Cart B

For Cart B with $m_B = 4\ kg$, the acceleration $a_B=\frac{F}{m_B}=\frac{F}{4}$.

Step4: Compare the accelerations

Dividing $a_A$ by $a_B$: $\frac{a_A}{a_B}=\frac{\frac{F}{2}}{\frac{F}{4}}=\frac{F}{2}\times\frac{4}{F} = 2$. So $a_A = 2a_B$. This shows that when the force is constant, the acceleration is inversely proportional to the mass.

(a) The acceleration of Cart A is twice the acceleration of Cart B. (b) When the applied force is constant, the acceleration is inversely proportional to the mass. That is, as the mass increases, the acceleration decreases, and vice - versa. Mathematically, from $F = ma$ (where $F$ is constant), $a=\frac{F}{m}$, so $a\propto\frac{1}{m}$.

Answer:

(a) The acceleration of Cart A is twice the acceleration of Cart B. (b) When the applied force is constant, acceleration is inversely proportional to mass.