Question

1. what is the acceleration of a 25 kg mass pushed by a 10 n force?
2. given a force of 100 n and an acceleration of 5 m/s², what is the mass?
3. how much force is required to accelerate a 50 kg mass at 2 m/s²?
4. what is the acceleration of an 18 kg mass pushed by a 9 n force?
5. find the acceleration of the 2 kg block in the following diagram.

Explanation:

Step1: Recall Newton's second - law formula

$F = ma$, where $F$ is force, $m$ is mass, and $a$ is acceleration. We can re - arrange it for different unknowns.

Step2: Solve question 12

Given $F = 10\ N$ and $m = 25\ kg$. Rearranging $F=ma$ for $a$, we get $a=\frac{F}{m}$. Substituting values: $a=\frac{10}{25}=0.4\ m/s^{2}$.

Step3: Solve question 13

Given $F = 100\ N$ and $a = 5\ m/s^{2}$. Rearranging $F = ma$ for $m$, we get $m=\frac{F}{a}$. Substituting values: $m=\frac{100}{5}=20\ kg$.

Step4: Solve question 14

Given $m = 50\ kg$ and $a = 2\ m/s^{2}$. Using $F = ma$, we substitute values: $F=50\times2 = 100\ N$.

Step5: Solve question 15

Given $F = 9\ N$ and $m = 18\ kg$. Rearranging $F = ma$ for $a$, we get $a=\frac{F}{m}$. Substituting values: $a=\frac{9}{18}=0.5\ m/s^{2}$.

Step6: Solve question 16

First, find the net force. The forces acting on the $2\ kg$ block are $F_{1}=4\ N$ and $F_{2}=8\ N$. The net force $F_{net}=8 - 4=4\ N$. Then, using $F = ma$ and rearranging for $a$, we have $a=\frac{F_{net}}{m}$. Substituting $F_{net}=4\ N$ and $m = 2\ kg$, we get $a=\frac{4}{2}=2\ m/s^{2}$.

Answer:

1. $0.4\ m/s^{2}$
2. $20\ kg$
3. $100\ N$
4. $0.5\ m/s^{2}$
5. $2\ m/s^{2}$