Question

1. using newtons second law, what would happen to the acceleration of the cart if the net force (σf) being applied to the cart remains unchanged but another 0.5 kg metal cylinder is added to the cart, increasing the carts mass? 9)
2. explain your answer! use the word ratio in your answer. 10)
3. if you performed this experiment on the moon, where the gravity is 1/6th that of earths, how would the results of this lab change? how would the results of this lab remain the same? (hint: what is providing the net force) how could you change the setup of this lab to ensure the results of this lab would remain unchanged on the moon? 11)

Explanation:

Step1: Recall Newton's Second Law

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

Step2: Analyze the change in mass

If $F$ is constant and $m$ increases (a $0.5$ kg metal cylinder is added to the cart), from the formula $a=\frac{F}{m}$, when the denominator $m$ increases while the numerator $F$ remains the same, the value of $a$ (acceleration) decreases.

Step3: Answer question 10

According to Newton's Second Law $a = \frac{F}{m}$, the acceleration $a$ is inversely proportional to the mass $m$ when the net - force $F$ is constant. The ratio of acceleration to mass is given by $\frac{a}{m}=\frac{F}{m^{2}}$. As the mass $m$ increases with a constant net - force $F$, the acceleration $a$ decreases because the ratio of net - force to mass determines the acceleration, and when mass goes up while force stays the same, the value of acceleration (the ratio of force to mass) goes down.

Step4: Answer question 11

The net - force in this experiment is likely not provided by gravity (assuming it's a horizontal pull or push and not a gravitational - pull related force for the motion in question). The results that depend on the relationship $F = ma$ (the acceleration - mass - force relationship) would remain the same on the moon because Newton's Second Law is a fundamental law of motion that is not affected by the gravitational field strength. However, if the net - force was due to the weight of an object (e.g., if the cart was on an inclined plane and the force was related to the component of gravitational force along the plane), the net - force would change on the moon since weight $W=mg$ and $g$ is $\frac{1}{6}$ of that on Earth. To ensure the results remain unchanged on the moon when the force is related to weight, we could use a non - gravitational source of force like a spring scale or a battery - powered motor to apply a constant force, or we could increase the mass of the objects involved in such a way that the product of mass and the reduced gravitational acceleration on the moon gives the same net - force as on Earth.

Answer:

1. The acceleration of the cart would decrease.
2. The acceleration is inversely proportional to the mass when the net - force is constant. The ratio of net - force to mass determines the acceleration. As mass increases with constant net - force, acceleration decreases.
3. Results based on $F = ma$ (non - gravitational force cases) remain the same. If force is related to weight, results change. To keep results the same, use non - gravitational force sources or adjust mass to account for the lower $g$ on the moon.