Question

f=ma worksheet1. how much force is required to accelerate a 2 kg mass at $3\\ \text{m/s}^2$?2. given a force of 100 n and an acceleration of $10\\ \text{m/s}^2$, what is the mass?3. what is the acceleration of a 10 kg mass pushed by a 5 n force?4. given a force of 88 n and an acceleration of $4\\ \text{m/s}^2$, what is the mass?5. how much force is required to accelerate a 12 kg mass at $5\\ \text{m/s}^2$?6. given a force of 10 n and an acceleration of $5\\ \text{m/s}^2$, what is the mass?7. how much force is required to accelerate a 5 kg mass at $20\\ \text{m/s}^2$?8. what is the acceleration of a 5 kg mass pushed by a 10 n force?9. given a force of 56 n and an acceleration of $7\\ \text{m/s}^2$, what is the mass?10. how much force is required to accelerate an 8 kg mass at $5\\ \text{m/s}^2$?11. what is the acceleration of a 24 kg mass pushed by a 6 n force?12. what is the acceleration of a 25 kg mass pushed by a 10 n force?13. given a force of 100 n and an acceleration of $5\\ \text{m/s}^2$, what is the mass?14. how much force is required to accelerate a 50 kg mass at $2\\ \text{m/s}^2$?15. what is the acceleration of an 18 kg mass pushed by a 9 n force?16. find the acceleration of the 2 kg block in the following diagram.17. find the acceleration of the 1 kg block in the following diagram

Explanation:

Step1: Recall core formula

The fundamental formula is $F = ma$, where $F$ = force (N), $m$ = mass (kg), $a$ = acceleration ($\text{m/s}^2$). Rearrange as needed: $m=\frac{F}{a}$, $a=\frac{F}{m}$.
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Problem 1: Calculate force

Substitute $m=2$, $a=3$ into $F=ma$
$F = 2 \times 3 = 6$

Problem 2: Calculate mass

Substitute $F=100$, $a=10$ into $m=\frac{F}{a}$
$m = \frac{100}{10} = 10$

Problem 3: Calculate acceleration

Substitute $F=5$, $m=10$ into $a=\frac{F}{m}$
$a = \frac{5}{10} = 0.5$

Problem 4: Calculate mass

Substitute $F=88$, $a=4$ into $m=\frac{F}{a}$
$m = \frac{88}{4} = 22$

Problem 5: Calculate force

Substitute $m=12$, $a=5$ into $F=ma$
$F = 12 \times 5 = 60$

Problem 6: Calculate mass

Substitute $F=10$, $a=5$ into $m=\frac{F}{a}$
$m = \frac{10}{5} = 2$

Problem 7: Calculate force

Substitute $m=5$, $a=20$ into $F=ma$
$F = 5 \times 20 = 100$

Problem 8: Calculate acceleration

Substitute $F=10$, $m=5$ into $a=\frac{F}{m}$
$a = \frac{10}{5} = 2$

Problem 9: Calculate mass

Substitute $F=56$, $a=7$ into $m=\frac{F}{a}$
$m = \frac{56}{7} = 8$

Problem 10: Calculate force

Substitute $m=8$, $a=5$ into $F=ma$
$F = 8 \times 5 = 40$

Problem 11: Calculate acceleration

Substitute $F=6$, $m=24$ into $a=\frac{F}{m}$
$a = \frac{6}{24} = 0.25$

Problem 12: Calculate acceleration

Substitute $F=10$, $m=25$ into $a=\frac{F}{m}$
$a = \frac{10}{25} = 0.4$

Problem 13: Calculate mass

Substitute $F=100$, $a=5$ into $m=\frac{F}{a}$
$m = \frac{100}{5} = 20$

Problem 14: Calculate force

Substitute $m=50$, $a=2$ into $F=ma$
$F = 50 \times 2 = 100$

Problem 15: Calculate acceleration

Substitute $F=9$, $m=18$ into $a=\frac{F}{m}$
$a = \frac{9}{18} = 0.5$

Problem 16: Net force then acceleration

Calculate net force: $F_{\text{net}} = 8 - 4 = 4$ N (left). Substitute $F_{\text{net}}=4$, $m=2$ into $a=\frac{F_{\text{net}}}{m}$
$a = \frac{4}{2} = 2$ $\text{m/s}^2$ (left)

Problem 17: Net force then acceleration

Horizontal forces cancel ($5-5=0$). Net force is vertical: $F_{\text{net}}=4$ N (down). Substitute $F_{\text{net}}=4$, $m=1$ into $a=\frac{F_{\text{net}}}{m}$
$a = \frac{4}{1} = 4$ $\text{m/s}^2$ (down)

Answer:

1. 6 N
2. 10 kg
3. $0.5 \text{ m/s}^2$
4. 22 kg
5. 60 N
6. 2 kg
7. 100 N
8. $2 \text{ m/s}^2$
9. 8 kg
10. 40 N
11. $0.25 \text{ m/s}^2$
12. $0.4 \text{ m/s}^2$
13. 20 kg
14. 100 N
15. $0.5 \text{ m/s}^2$
16. $2 \text{ m/s}^2$ to the left
17. $4 \text{ m/s}^2$ downward